General functions practice
Evaluate twelve polynomial and exponential functions. Choose numbers, variable expressions or a mixture, with exact answers and substitution steps.
Ready-made English PDF · fixed settings
Customization below makes a separate PDF.
Fixed English ready-made files. Custom settings below apply only to the configured PDF.
Ready to print
Substitute the entire input wherever the variable appears. Evaluate numerical inputs exactly; expand and collect polynomial expressions and simplify exponential exponents.
Download the practice pages alone, or include a separate answer key or teacher model. Longer activities may use more than one page.
Customize this worksheetPaper sizes and printing help · More general functions activities
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
Substitute a number or a complete expression into a function, then evaluate or simplify the result.
Worked example
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 it yours
Choose your options, update the preview, then download the exact same pages.
Choose the practice settings, update the preview and print the same questions with a separate answer key.
A useful next step
Algebraic expressions
Substitute a given value and evaluate expressions with one variable. Choose addition, subtraction, grouped products or exact division, with whole-number or signed integer inputs.
Preview and download
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.
Preview and download
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.
Preview and download
