Read the inputs. Compare the outputs.
Find an output by substituting a number or an expression into a function. Combine two functions, practice composition, or calculate a rate from a table, a graph or a symbolic difference quotient.
Choose a practice sheetAvailable practice
Start with mappings, ordered pairs and continuous graphs to classify functions and read domains and ranges. Continue with evaluation, operations, rates, inverses and graphing. Every activity includes a separate worked key.
General functions
Classify eight mapping diagrams as functions or nonfunctions. Choose two to five numeric or letter values on each side, with four of each classification and a separate answer key.
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General functions
Find the domain and range of ten five-pair relations. Choose negative or nonnegative coordinates, control repeats independently and optionally classify each relation as a function.
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General functions
Apply the vertical line test to eight finite graph relations. Choose lines, polynomials, special curves, horizontal parabolas or rotated curves, with balanced endpoints and a separate key.
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General functions
Read finite domain and range intervals from eight varied relation graphs. Practice open and closed extrema and optionally apply the vertical line test.
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General functions
Evaluate twelve polynomial and exponential functions. Choose numbers, variable expressions or a mixture, with exact answers and substitution steps.
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General functions
Add, subtract, multiply, divide and compose polynomial functions. Choose numbers, variables or mixed inputs, with ten questions and a separate worked answer key.
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General functions
Find average rates from six function tables. Choose 6 or 12 questions, print Letter or A4, and check each result with a separate worked answer key.
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General functions
Simplify eight difference quotients with polynomial, factored and rational functions. Choose two inputs or an increment, add a formula reminder and print worked answers.
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General functions
Read four function graphs and estimate their average rates of change. Choose linear, quadratic, cubic, sine or exponential curves, with secants and worked answers.
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General functions
Identify inverse pairs or find inverse functions in twelve original questions. Practice linear functions and powers with explicit domains, exact radicals and worked answers.
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General functions
Find and graph four inverse functions. Choose fractional or integer linear rules, lines through the origin, quadratic branches and cubic functions, with completed graph keys.
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General functions
Graph four quadratic functions in vertex form on blank coordinate grids. Each sheet includes every leading coefficient from −2, −1, 1 and 2, with a separate completed graph key.
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General functions
Find the domain and range, then graph eight transformed square-root and cube-root functions on unit grids. Choose square roots, cube roots or balanced mixed practice with separate completed graph keys.
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General functions
Graph eight exponential functions or write equations from curves with exact marked points. Compare growth, decay and translations on fixed unit grids with separate answer keys.
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General functions
Find exact domains and all-real ranges, then graph eight logarithmic functions with vertical asymptotes on fixed square grids. Includes affine arguments, fractional boundaries and separate answer keys.
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General functions
Find inverses in logarithmic, exponential or mixed directions across six exact forms. Every problem prints the real domain needed for a single-valued inverse, with separate exact answer keys.
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General functions
Graph four expanded quadratic inequalities on blank coordinate grids. Compare unit and nonunit leading coefficients, both opening directions and all four strict or inclusive relations.
Preview and downloadSix questions, each using a different table. Focus on choosing the correct rows and subtraction order.
Open this practice →Twelve questions on the same six tables. Compare rates on two different intervals in each table.
Open this practice →The input in f(2x + 1) is the complete expression 2x + 1. Substitute it everywhere the variable occurs and keep the parentheses until you have expanded the powers.
Evaluate twelve numerical inputs, including signed values and exact fractions from negative exponents.
Open this practice →Replace the variable with a shifted, scaled, squared or affine expression, then simplify.
Open this practice →Use six numerical and six expression inputs to practice choosing the right substitution steps.
Open this practice →Adding or multiplying functions uses the same input in both. Composition works in stages: in (f ∘ g)(x), calculate g first and substitute its output into f. A quotient also needs its original denominator to stay nonzero.
Start with numerical inputs and practice addition, subtraction, multiplication and exact division.
Open this practice →Compose polynomial functions with variable inputs, including a shifted input inside the inner function.
Open this practice →Mix all five operations with five numerical and five variable inputs. Keep quotient restrictions visible.
Open this practice →Practice with expanded and factored polynomials, reciprocal functions and rational functions. The two inputs can be x and a, or x and x + h. Simplifying changes the expression, but it does not remove the original restrictions.
Compare inputs x and a with the formula printed above the eight questions.
Open this practice →Substitute x + h into the same function and simplify. Keep h nonzero after cancellation.
Open this practice →Practice the increment form without a printed reminder; the separate key still shows every step.
Open this practice →A secant joins two points on a curve. Its slope describes average change across the interval, even when the curve bends or turns between them. Read the two endpoints before calculating.
Read a linear, quadratic, cubic and sine graph. Compare average change with the shape between the endpoints.
Open this practice →Practice four exponential graphs with increasing and decreasing curves. The key marks the two points and their secant.
Open this practice →Compare quadratic, cubic, sine and exponential graphs using the same endpoint method.
Open this practice →An inverse swaps inputs and outputs. A linear rule with nonzero slope has an inverse on all real numbers; an even power first needs a one-to-one branch. Read the printed domains before choosing a root sign.
Twelve pairs, with six true inverses and six incorrect matches. Use the printed domains and check the compositions.
Open this practice →Find twelve inverses of linear functions and powers. Read each even-power branch before choosing the root sign.
Open this practice →Identify six pairs, then find six inverses. The key includes exact counterexamples and algebraic steps.
Open this practice →Find the inverse formula, then reflect points across y = x. A restricted quadratic branch becomes a square-root graph; a cubic becomes a real cube-root graph. Keep the stated domains visible.
Compare fractional and integer slopes, including lines through the origin, on four blank coordinate grids.
Open this practice →Graph four restricted parabolas and their square-root inverses. Check the printed branch and reflected endpoint.
Open this practice →Graph shifted and scaled cubics and their real cube-root inverses, including negative scales.
Open this practice →For inputs a and b, the average rate is (f(b) − f(a)) ÷ (b − a). The numerator measures output change and the denominator measures input change.
Either order works when both differences follow that order. Reversing only one difference changes the sign and gives the wrong rate.
Table rows can have unequal gaps. Always use the actual x values rather than counting the rows between them.
These existing activities address different parts of the process: finding outputs, calculating slope from coordinates and reading a graph.
Function table
Substitute five inputs into each of twelve linear rules. Choose whole or fractional slopes, signed or nonnegative inputs, and decimal or exact fraction answers.
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Linear functions
Calculate exact slopes from ten pairs of integer-coordinate points. Practice signed differences and reduced fractions, with a separate key that explains the slope calculation.
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Linear functions
Read eight graphed lines and find each exact slope. Use the coordinate scale to compare rise and run, then check a separate answer key with worked calculations.
Preview and downloadThe average rate between two function values is the slope of the line joining those two points. A linear function has the same rate on every interval; other functions can have different rates on different intervals.
No. Both settings have six tables with six data pairs each. The 12-question setting asks about two different intervals in every table.
Function evaluation uses exact results, including fractions. For the table-rate activity, keep the displayed values exact through subtraction and division, then round the final rate to the nearest hundredth when needed. Its key clearly marks approximations.
These worksheets use halfway rounding away from zero. For example, 1.235 rounds to 1.24 and −1.235 to −1.24. This rule is stated on the printed worksheet.
Yes. Copy the settings link to preserve the seed and options. Changing paper size or print language keeps the mathematical data. In table-rate practice, increasing to 12 questions also preserves each table and its first question.
Choose this practice by skill. Course names and grade placement vary between curricula; this collection does not claim alignment with a specific curriculum.
Combine function work with signed arithmetic, expressions and complex-number practice when those skills match the lesson.
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