# Functions and equations

Here is a list of all of the skills that cover functions and equations! These skills are organized by grade, and you can move your mouse over any skill name to preview the skill. To start practising, just click on any link. IXL will track your score, and the questions will automatically increase in difficulty as you improve!

## Grade 2 skills

- E.8 Addition input/output tables - sums to 20
- F.8 Subtraction input/output tables - up to 18
- G.7 Addition input/output tables - up to two digits
- H.7 Subtraction input/output tables - up to two digits
- I.3 Addition input/output tables - up to three digits
- J.3 Subtraction input/output tables - up to three digits
- X.5 Input/output tables - write the rule - up to 20
- X.10 Input/output tables - write the rule - up to 100

## Grade 3 skills

- C.2 Addition input/output tables - up to three digits
- C.10 Addition input/output tables - four or more digits
- D.2 Subtraction input/output tables - up to three digits
- D.8 Subtraction input/output tables - four or more digits
- H.4 Multiplication input/output tables
- L.3 Division input/output tables
- O.1 Identify equations
- O.2 Solve for the variable
- O.3 Write variable equations to represent word problems

## Grade 5 skills

- M.9 Multiply fractions by whole numbers: input/output tables
- R.4 Write variable equations: word problems
- R.5 Solve equations with whole numbers
- R.6 Find a value using two-variable equations
- R.7 Complete a table for a two-variable relationship
- R.8 Complete a table from a graph
- R.9 Graph a two-variable relationship
- R.10 Write a two-variable equation

## Grade 6 skills

- X.1 Does x satisfy an equation?
- X.2 Which x satisfies an equation?
- X.3 Write an equation from words
- X.4 Model and solve equations using algebra tiles
- X.5 Write and solve equations that represent diagrams
- X.6 Solve one-step equations with whole numbers
- X.7 Solve one-step equations with decimals
- X.8 Solve one-step equations: word problems
- Y.1 Does (x, y) satisfy an equation?
- Y.2 Identify independent and dependent variables
- Y.3 Solve word problems involving two-variable equations
- Y.4 Complete a table for a two-variable relationship
- Y.5 Write a two-variable equation
- Y.6 Identify the graph of an equation

## Grade 7 skills

- M.2 Write equations for proportional relationships from tables
- M.4 Find the constant of proportionality from a graph
- M.5 Write equations for proportional relationships from graphs
- M.6 Identify proportional relationships
- M.7 Interpret graphs of proportional relationships
- T.11 Solve equations using properties
- U.1 Which x satisfies an equation?
- U.2 Write an equation from words
- U.3 Model and solve equations using algebra tiles
- U.4 Write and solve equations that represent diagrams
- U.5 Solve one-step equations
- U.6 Solve two-step equations
- U.7 Solve equations: word problems
- U.8 Solve equations involving like terms
- U.9 Solve equations: complete the solution
- V.1 Does (x, y) satisfy the equation?
- V.2 Identify independent and dependent variables
- V.3 Solve word problems involving two-variable equations
- V.4 Complete a table for a two-variable relationship
- V.5 Write a two-variable equation
- V.6 Identify the graph of an equation
- V.7 Graph a two-variable equation
- V.8 Interpret a graph: word problems
- V.9 Write an equation from a graph using a table

## Grade 8 skills

- G.9 Solve equations involving squares and square roots
- J.2 Write equations for proportional relationships from tables
- J.4 Find the constant of proportionality from a graph
- J.5 Write equations for proportional relationships from graphs
- J.6 Identify proportional relationships
- J.8 Interpret graphs of proportional relationships
- J.9 Write and solve equations for proportional relationships
- X.1 Which x satisfies an equation?
- X.2 Write an equation from words
- X.3 Model and solve equations using algebra tiles
- X.4 Write and solve equations that represent diagrams
- X.6 Solve one-step equations
- X.7 Solve two-step equations
- X.8 Solve equations involving like terms
- X.9 Solve equations: complete the solution
- X.10 Solve equations: word problems
- Y.1 Does (x, y) satisfy the linear function?
- Y.4 Complete a table for a linear function
- Y.5 Complete a table and graph a linear function
- Y.6 Graph a line from an equation
- Y.7 Interpret the graph of a linear function: word problems
- Y.8 Write a linear function from a table
- Y.9 Write linear functions: word problems

## Grade 9 skills

- K.4 Rate of travel: word problems
- K.5 Weighted averages: word problems
- M.4 Write variable equations
- M.5 Does x satisfy the equation?
- M.6 Solve equations using order of operations
- N.1 Model and solve equations using algebra tiles
- N.2 Write and solve equations that represent diagrams
- N.3 Solve one-step linear equations
- N.4 Solve two-step linear equations
- N.5 Solve advanced linear equations
- N.6 Solve equations with variables on both sides
- N.7 Solve equations: complete the solution
- N.8 Find the number of solutions
- N.10 Solve linear equations: word problems
- N.11 Solve linear equations: mixed review
- P.7 Scatter plots: line of best fit
- Q.1 Relations: convert between tables, graphs, mappings and lists of points
- Q.2 Identify independent and dependent variables
- Q.3 Identify functions
- Q.4 Identify functions: vertical line test
- Q.5 Find values using function graphs
- Q.6 Evaluate a function
- Q.7 Evaluate a function: plug in an expression
- Q.8 Complete a function table from a graph
- Q.9 Complete a function table from an equation
- Q.10 Interpret the graph of a function: word problems
- R.1 Identify proportional relationships
- R.2 Find the constant of variation
- R.3 Graph a proportional relationship
- R.4 Write direct variation equations
- R.5 Write and solve direct variation equations
- S.1 Identify linear functions
- S.2 Find the slope of a graph
- S.3 Find the slope from two points
- S.5 Slope-intercept form: find the slope and y-intercept
- S.6 Slope-intercept form: graph an equation
- S.7 Slope-intercept form: write an equation from a graph
- S.8 Slope-intercept form: write an equation
- S.9 Slope-intercept form: write an equation from a table
- S.10 Slope-intercept form: write an equation from a word problem
- S.11 Linear equations: solve for y
- S.12 Write linear functions to solve word problems
- S.13 Complete a table and graph a linear function
- S.14 Compare linear functions: graphs, tables and equations
- S.15 Write equations in standard form
- S.16 Standard form: find x- and y-intercepts
- S.17 Standard form: graph an equation
- S.18 Equations of horizontal and vertical lines
- S.19 Graph a horizontal or vertical line
- S.20 Point-slope form: graph an equation
- S.21 Point-slope form: write an equation
- S.22 Point-slope form: write an equation from a graph
- S.23 Slopes of parallel and perpendicular lines
- S.24 Write an equation for a parallel or perpendicular line
- S.25 Transformations of linear functions
- T.1 Is (x, y) a solution to the system of equations?
- T.2 Solve a system of equations by graphing
- T.3 Solve a system of equations by graphing: word problems
- T.4 Find the number of solutions to a system of equations by graphing

## Grade 10 skills

- G.1 Model and solve equations using algebra tiles
- G.2 Write and solve equations that represent diagrams
- G.3 Solve one-step linear equations
- G.4 Solve two-step linear equations
- G.5 Solve advanced linear equations
- G.6 Solve equations with variables on both sides
- G.7 Solve equations: complete the solution
- G.8 Find the number of solutions
- G.10 Solve linear equations: word problems
- G.11 Solve linear equations: mixed review
- I.7 Scatter plots: line of best fit
- J.1 Relations: convert between tables, graphs, mappings and lists of points
- J.2 Domain and range of relations
- J.3 Identify independent and dependent variables
- J.4 Identify functions
- J.5 Identify functions: vertical line test
- J.6 Find values using function graphs
- J.7 Evaluate a function
- J.8 Evaluate a function: plug in an expression
- J.9 Complete a function table from a graph
- J.10 Complete a function table from an equation
- J.11 Interpret the graph of a function: word problems
- K.1 Identify proportional relationships
- K.2 Find the constant of variation
- K.3 Graph a proportional relationship
- K.4 Write direct variation equations
- K.5 Write and solve direct variation equations
- K.6 Identify direct variation and inverse variation
- K.7 Write inverse variation equations
- K.8 Write and solve inverse variation equations
- L.1 Identify linear functions
- L.2 Find the slope of a graph
- L.3 Find the slope from two points
- L.5 Slope-intercept form: find the slope and y-intercept
- L.6 Slope-intercept form: graph an equation
- L.7 Slope-intercept form: write an equation from a graph
- L.8 Slope-intercept form: write an equation
- L.9 Slope-intercept form: write an equation from a table
- L.10 Slope-intercept form: write an equation from a word problem
- L.11 Write linear functions to solve word problems
- L.12 Complete a table and graph a linear function
- L.13 Compare linear functions: graphs, tables and equations
- L.14 Write equations in standard form
- L.15 Standard form: find x- and y-intercepts
- L.16 Standard form: graph an equation
- L.17 Equations of horizontal and vertical lines
- L.18 Graph a horizontal or vertical line
- L.19 Point-slope form: graph an equation
- L.20 Point-slope form: write an equation
- L.21 Point-slope form: write an equation from a graph
- L.22 Slopes of parallel and perpendicular lines
- L.23 Write an equation for a parallel or perpendicular line
- L.26 Transformations of linear functions
- M.1 Is (x, y) a solution to the system of equations?
- M.2 Solve a system of equations by graphing
- M.3 Solve a system of equations by graphing: word problems
- M.4 Find the number of solutions to a system of equations by graphing
- M.5 Find the number of solutions to a system of equations
- M.6 Classify a system of equations by graphing
- M.7 Classify a system of equations
- M.8 Solve a system of equations using substitution
- M.9 Solve a system of equations using substitution: word problems
- M.10 Solve a system of equations using elimination
- M.11 Solve a system of equations using elimination: word problems
- M.12 Solve a system of equations using any method
- M.13 Solve a system of equations using any method: word problems
- Q.1 Characteristics of quadratic functions
- Q.2 Complete a function table: quadratic functions
- Q.3 Solve a quadratic equation using square roots
- Q.4 Solve a quadratic equation using the zero product property
- Q.5 Solve a quadratic equation by factoring
- Q.7 Solve a quadratic equation by completing the square
- Q.8 Solve a quadratic equation using the quadratic formula
- Q.9 Using the discriminant
- S.1 Identify linear, quadratic and exponential functions from graphs
- S.2 Identify linear, quadratic and exponential functions from tables
- S.3 Write linear, quadratic and exponential functions
- S.4 Linear functions over unit intervals
- S.5 Exponential functions over unit intervals
- S.6 Describe linear and exponential growth and decay
- T.1 Rational functions: asymptotes and excluded values
- T.7 Solve rational equations

## Grade 11 skills

- B.1 Solve linear equations
- B.2 Solve linear equations: word problems
- B.3 Solve absolute value equations
- B.4 Graph solutions to absolute value equations
- C.8 Graph solutions to absolute value inequalities
- D.1 Domain and range
- D.2 Identify functions
- D.3 Evaluate functions
- D.4 Find values using function graphs
- D.5 Complete a table for a function graph
- D.6 Find the slope of a linear function
- D.7 Graph a linear function
- D.8 Write the equation of a linear function
- D.9 Linear functions over unit intervals
- E.1 Is (x, y) a solution to the system of equations?
- E.2 Solve a system of equations by graphing
- E.3 Solve a system of equations by graphing: word problems
- E.7 Solve a system of equations using substitution: word problems
- E.8 Solve a system of equations using elimination
- E.9 Solve a system of equations using elimination: word problems
- E.10 Solve a system of equations using any method
- E.11 Solve a system of equations using any method: word problems
- E.12 Solve a non-linear system of equations
- H.1 Characteristics of quadratic functions
- H.2 Complete a function table: quadratic functions
- H.3 Find a quadratic function
- H.4 Graph a quadratic function
- H.5 Match quadratic functions and graphs
- H.6 Solve a quadratic equation using square roots
- H.7 Solve a quadratic equation using the zero product property
- H.8 Solve a quadratic equation by factoring
- H.9 Complete the square
- H.10 Solve a quadratic equation using the quadratic formula
- H.11 Using the discriminant
- K.12 Domain and range of radical functions
- K.13 Solve radical equations
- M.1 Rational functions: asymptotes and excluded values
- M.7 Solve rational equations
- N.5 Exponential functions over unit intervals
- N.6 Describe linear and exponential growth and decay

## Grade 12 skills

- A.1 Domain and range
- A.2 Identify functions
- A.3 Find the slope of a linear function
- A.4 Graph a linear function
- A.5 Write the equation of a linear function
- A.6 Linear functions over unit intervals
- A.7 Evaluate functions
- A.8 Find values using function graphs
- A.9 Complete a table for a function graph
- A.10 Add, subtract, multiply and divide functions
- A.11 Composition of functions
- A.12 Identify inverse functions
- A.13 Find values of inverse functions from tables
- A.14 Find values of inverse functions from graphs
- A.15 Find inverse functions and relations
- A.16 Identify graphs of continuous functions
- B.1 Translations of functions
- B.2 Reflections of functions
- B.3 Dilations of functions
- B.4 Transformations of functions
- B.5 Function transformation rules
- B.6 Describe function transformations
- C.1 Characteristics of quadratic functions
- C.2 Find the maximum or minimum value of a quadratic function
- C.3 Graph a quadratic function
- C.4 Match quadratic functions and graphs
- C.5 Solve a quadratic equation using square roots
- C.6 Solve a quadratic equation by factoring
- C.7 Solve a quadratic equation by completing the square
- C.8 Solve a quadratic equation using the quadratic formula
- C.9 Using the discriminant
- D.9 Match polynomials and graphs
- D.11 Solve equations with sums and differences of cubes
- D.13 Solve equations using a quadratic pattern
- E.1 Rational functions: asymptotes and excluded values
- E.2 Solve rational equations
- E.3 Check whether two rational functions are inverses
- G.9 Exponential functions over unit intervals
- G.10 Describe linear and exponential growth and decay
- H.1 Domain and range of radical functions
- H.2 Solve radical equations
- J.1 Solve a system of equations by graphing
- J.2 Solve a system of equations by graphing: word problems
- J.3 Classify a system of equations
- J.4 Solve a system of equations using substitution
- J.5 Solve a system of equations using substitution: word problems
- J.6 Solve a system of equations using elimination
- J.7 Solve a system of equations using elimination: word problems
- J.8 Solve a system of equations in three variables using substitution
- J.9 Solve a system of equations in three variables using elimination
- J.10 Determine the number of solutions to a system of equations in three variables
- O.1 Find properties of sine functions
- O.5 Find properties of cosine functions
- P.1 Complementary angle identities
- P.2 Symmetry and periodicity of trigonometric functions
- P.3 Trigonometric identities I
- P.4 Trigonometric identities II
- AA.8 Find the equation of a regression line

## Calculus skills

- A.1 Find values of functions from graphs
- A.2 Add, subtract, multiply and divide functions
- A.3 Composition of functions
- A.4 Identify inverse functions
- A.5 Find values of inverse functions from tables
- A.6 Find values of inverse functions from graphs
- A.7 Find inverse functions and relations
- B.1 Function transformation rules
- B.2 Translations of functions
- B.3 Reflections of functions
- B.4 Dilations of functions
- B.5 Transformations of functions
- B.6 Describe function transformations
- C.8 Find properties of sine functions
- C.12 Find properties of cosine functions
- D.9 Describe linear and exponential growth and decay
- E.1 Find limits using graphs
- E.2 Find one-sided limits using graphs
- E.3 Determine if a limit exists
- F.1 Find limits using addition, subtraction and multiplication laws
- F.2 Find limits using the division law
- F.3 Find limits using power and root laws
- F.4 Find limits using limit laws
- F.5 Find limits of polynomials and rational functions
- F.6 Find limits involving factorization and rationalization
- F.7 Find limits involving absolute value functions
- F.8 Find limits involving trigonometric functions
- G.1 Find limits at vertical asymptotes using graphs
- G.2 Determine end behaviour using graphs
- G.3 Determine end behaviour of polynomial and rational functions
- H.1 Find the limit at a vertical asymptote of a rational function I
- H.2 Find the limit at a vertical asymptote of a rational function II
- I.1 Identify graphs of continuous functions
- I.2 Determine continuity using graphs
- I.3 Determine one-sided continuity using graphs
- I.4 Find and analyze points of discontinuity using graphs
- I.5 Determine continuity on an interval using graphs
- I.6 Determine the continuity of a piecewise function at a point
- I.7 Make a piecewise function continuous
- I.8 Intermediate Value Theorem
- J.1 Average rate of change I
- J.2 Average rate of change II
- J.3 Find instantaneous rates of change
- J.4 Velocity as a rate of change
- J.5 Find values of derivatives using limits
- J.6 Find the slope of a tangent line using limits
- J.7 Find equations of tangent lines using limits
- K.1 Sum and difference rules
- K.2 Product rule
- K.3 Quotient rule
- K.4 Power rule I
- K.5 Power rule II
- K.6 Chain rule
- K.7 Inverse function rule
- L.1 Find derivatives of polynomials
- L.2 Find derivatives of rational functions
- L.3 Find derivatives of trigonometric functions I
- L.4 Find derivatives of trigonometric functions II
- L.5 Find derivatives of exponential functions
- L.6 Find derivatives of logarithmic functions
- L.7 Find derivatives of inverse trigonometric functions
- L.8 Find derivatives of radical functions
- L.9 Find derivatives using the product rule I
- L.10 Find derivatives using the product rule II
- L.11 Find derivatives using the quotient rule I
- L.12 Find derivatives using the quotient rule II
- L.13 Find derivatives using the chain rule I
- L.14 Find derivatives using the chain rule II
- M.1 Find derivatives using implicit differentiation
- M.2 Find tangent lines using implicit differentiation
- M.3 Find derivatives using logarithmic differentiation
- N.1 Find higher derivatives of polynomials
- N.2 Find higher derivatives of rational and radical functions
- N.3 Find second derivatives of trigonometric, exponential and logarithmic functions
- N.4 Find higher derivatives using patterns