General functions practice

Evaluating functions worksheets

Evaluate twelve polynomial and exponential functions. Choose numbers, variable expressions or a mixture, with exact answers and substitution steps.

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Substitute the entire input wherever the variable appears. Evaluate numerical inputs exactly; expand and collect polynomial expressions and simplify exponential exponents.

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One function. A different kind of input.

Choose twelve numerical inputs, twelve variable expressions, or a mixture with six of each. Practice linear, quadratic, cubic and exponential functions. Each question earns one mark.

With a numerical input, calculate an exact value. With an expression input, replace every variable with the entire expression, expand polynomial products and collect like terms. Exponential answers may keep a power with a simplified exponent.

The separate key repeats each question and shows the substitution before the answer. Parentheses matter: (−3)² is positive, while −3² has a negative sign outside the power. Negative numerical exponents produce exact fractions.

Learning objective

What this activity builds

Substitute a number or a complete expression into a function, then evaluate or simplify the result.

Worked example

If f(x) = x² + 3, find f(2x + 1).

f(2x + 1) = (2x + 1)² + 3 = 4x² + 4x + 4.

Replace x with the entire expression in parentheses. Squaring a sum produces a middle term: (2x + 1)² = 4x² + 4x + 1. Add the remaining constant after expanding.

Teaching notes

Make the practice count

  • Underline the input inside the function notation.
  • Replace every occurrence of the variable, keeping a substituted sum in parentheses.
  • Evaluate powers before multiplication and addition.
  • Use a reciprocal for a negative exponent; keep the fraction exact.
  • Distinguish (−3)² = 9 from −3² = −9.
  • For an exponential function with a symbolic input, simplify the exponent instead of inventing a numerical value.

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Configured PDF · Evaluating Single Functions · US Letter

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Math SheetNameScore/ 12TeacherDateEvaluating Single FunctionsEvaluate each function at the given argument. Simplify exactly.1.q(x) =-9x2-11q(y-5)2.s(x) =-54·xs(0)3.g(x) =34·x-2g(-2)4.f(x) =-11x2-8f(7)5.j(x) =11xj(y+3)6.m(x) =x3-8x2m(4y)7.p(x) =x3+10x2p(-3)8.h(x) =2xh(-9)9.u(x) =-9x2+10xu(y2)10.k(x) =9x2+10xk(1)11.v(x) =4x-1v(y-1)12.r(x) =-24·xr(-2y)math-sheet.comPage 1 / 1

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