Graph f(x) = 2x + 2 for the domain -3, 0, 1, 3

(-3, -4), (0, 2), (1, 4), (3, 8)

Algebra 2 evaluating functions worksheet

f(3) means put 3 wherever x is and work it out. The input can be a number, an expression like a + 2, or a value read from a table. Parentheses around whatever goes in save most of the sign mistakes.



Sigma Prep · sigmaprep.io/worksheets Name Evaluating Functions Date Period Evaluate, or solve, as asked. Given $f (x) = - 8 x^{2} + 9 x - 8$ , find $f (7)$ Given $f (x) = - x - 1$ , find $f (- a)$ Given $f (x) = \sqrt{x + 47}$ , find $f (2)$ Use the graph of $f$ . Find $f (1) + f (4)$ Given $f (x) = - 9 x^{2} + 9 x + 8$ , find $f (- 6)$ Given $f (x) = x^{2} - 3 x - 3$ , find $f (3)$ Given $f (x) = \sqrt{x + 54}$ , find $f (- 5)$ Use the graph of $f$ . Find $f (7) + f (5)$ Given $f (x) = 9 x^{2} - 9 x - 9$ , find $f (6)$ Given $f (x) = - 5 x + 6$ , find $f (2 a)$ Given $g (x) = ∣ - 2 x - 6 ∣$ , find $g (0)$ Use the graph of $f$ . Find $f (- 5) + f (- 7)$ Given $f (x) = - 8 x^{2} + 8 x - 7$ , find $f (6)$ Given $f (x) = 5 x - 3$ , find $f (4 a)$ Given $f (x) = 3^{x}$ , find $f (3)$ Use the graph of $f$ . Find $f (8) + f (- 5)$ Given $f (x) = - 7 x^{2} + 7 x + 8$ , find $f (- 6)$ Given $f (x) = - 2 x + 6$ , find $f (2 a)$ Given $f (x) = \sqrt{x + 81}$ , find $f (0)$ Use the graph of $f$ . Find $f (5) + f (- 8)$ Free math worksheets at sigmaprep.io/worksheets© 2026 Sigma Prep



Sigma Prep · sigmaprep.io/worksheets Name Evaluating FunctionsAnswer keyVersion 1 Date Period Evaluate, or solve, as asked. Given $f (x) = - 8 x^{2} + 9 x - 8$ , find $f (7)$ $- 337$ Given $f (x) = - x - 1$ , find $f (- a)$ $a - 1$ Given $f (x) = \sqrt{x + 47}$ , find $f (2)$ $7$ Use the graph of $f$ . Find $f (1) + f (4)$ $- 7$ Given $f (x) = - 9 x^{2} + 9 x + 8$ , find $f (- 6)$ $- 370$ Given $f (x) = x^{2} - 3 x - 3$ , find $f (3)$ $- 3$ Given $f (x) = \sqrt{x + 54}$ , find $f (- 5)$ $7$ Use the graph of $f$ . Find $f (7) + f (5)$ $9$ Given $f (x) = 9 x^{2} - 9 x - 9$ , find $f (6)$ $261$ Given $f (x) = - 5 x + 6$ , find $f (2 a)$ $- 10 a + 6$ Given $g (x) = ∣ - 2 x - 6 ∣$ , find $g (0)$ $6$ Use the graph of $f$ . Find $f (- 5) + f (- 7)$ $3$ Given $f (x) = - 8 x^{2} + 8 x - 7$ , find $f (6)$ $- 247$ Given $f (x) = 5 x - 3$ , find $f (4 a)$ $20 a - 3$ Given $f (x) = 3^{x}$ , find $f (3)$ $27$ Use the graph of $f$ . Find $f (8) + f (- 5)$ $- 9$ Given $f (x) = - 7 x^{2} + 7 x + 8$ , find $f (- 6)$ $- 286$ Given $f (x) = - 2 x + 6$ , find $f (2 a)$ $- 4 a + 6$ Given $f (x) = \sqrt{x + 81}$ , find $f (0)$ $9$ Use the graph of $f$ . Find $f (5) + f (- 8)$ $0$ Free math worksheets at sigmaprep.io/worksheets© 2026 Sigma Prep

How to do these

Given $f (x) = x^{2} + 2 x$ , find $f (a + 3)$

Replace every x with (a + 3).
(a + 3)² is a² + 6a + 9, and 2(a + 3) is 2a + 6.
Add them.

The answer is $a^{2} + 8 a + 15$ .

Where students go wrong

Dropping the parentheses: f(-2) for x² becomes -2² = -4 instead of (-2)² = 4. The input goes in whole.

Also called function notation, evaluate f(x), function tables or input and output.

What you can put on this worksheet

Evaluate a function at a value: Given $f (x) = - 3 x + 5$ , find $f (2)$ → $- 1$
A number, then an expression, as the input: Given $f (x) = 4 x$ , find $f (- 2)$ → $- 8$
From a table: Use the table to find $f (3)$
$\begin{array}{cccccc} x & - 1 & 0 & 1 & 2 & 3 \\ f (x) & 4 & - 8 & 0 & 1 & - 5 \end{array}$ → $- 5$
Roots, absolute values, fractions and powers: Given $g (x) = ∣ 3 x - 5 ∣$ , find $g (1)$ → $2$
Find the input that gives an output: Given $f (x) = 3 x + 1$ , solve $f (x) = - 14$ → ${- 5}$
From a graph: Use the graph of $f$ . Find $f (- 7)$ → $- 4$
Absolute value with a number outside the bars: Given $g (x) = ∣ x - 5 ∣ - 5$ , find $g (9)$ → $- 1$
A fraction or a decimal for the input: Given $h (x) = - 8 x + 6$ , find $h (\frac{1}{5})$ → $\frac{22}{5}$
Graph on a given domain: Graph $f (x) = 2 x + 2$ for the domain ${- 3, 0, 1, 3}$ → $(- 3, - 4),$ $(0, 2),$ $(1, 4),$ $(3, 8)$

Questions about these worksheets

Yes. Every evaluating functions sheet is free to print and free to download as a PDF. There is no account to make, no email to hand over and no limit on how many you take.

Yes. The answer key prints on a second page, and you can choose whether it shows each question beside its answer or just the answers in a list.

Yes. Print straight from the page, or download the PDF and print that. The sheet is laid out for paper rather than squeezed off a screen, so there is room to work under each question, and the answer key comes out on its own page.

Algebra 2 is usually taken around 10th or 11th grade, though schools vary and plenty of students meet it earlier or later. Pick the difficulty rather than the grade: the easy level suits a first lesson on it, the hard level suits review before a test.

Yes, as many as you like. The questions are built fresh each time rather than picked from a fixed set of files, so pressing Generate gives a new sheet. That is what you want for a second class, a retake, or two students sitting next to each other.

That is the closest comparison, and Kuta Software is good software. It is also paid software you install on a computer. These worksheets run in a browser tab for free, with no account and nothing to install. Like Kuta, the evaluating functions questions are generated when you ask for them rather than pulled from a fixed set of files, so two classes never get the same sheet, and the answer key comes with it.

Yes. There are three levels, and you can tick more than one for a sheet that mixes them, in which case the questions come out easiest first. The harder levels are not just larger numbers: they ask for something the easy ones do not.

You pick from 9: evaluate a function at a value, a number, then an expression, as the input, from a table, roots, absolute values, fractions and powers, find the input that gives an output, from a graph, absolute value with a number outside the bars, a fraction or a decimal for the input and graph on a given domain. Tick as many as you want and set how many of each, or let it spread them evenly.

Dropping the parentheses: f(-2) for x² becomes -2² = -4 instead of (-2)² = 4. The input goes in whole.

Algebra 2 evaluating functions worksheet

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Evaluating Functions

Evaluating FunctionsAnswer keyVersion 1

How to do these

Where students go wrong

What you can put on this worksheet

Questions about these worksheets

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