Grade 11 · Math · Algebra 2

11th grade Inverse functions from tables and graphs worksheet

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Inverse functions from tables and graphs

Grade 11 Math Worksheet - Challenge Me

NameDate

Circle the best answer, or write your answer on the line.

Milo works in pencil with the graph of f and g(x) = -x² + 4. What is g(f⁻¹(6))?
On a puzzle card, Noah sees the graph of f and g(x) = -3x + 2. What is g(f⁻¹(5))?
3.
Pia's worksheet shows the graph of f, a segment from (-2, 1) to (4, 13). What is the domain of f⁻¹?
- -2 ≤ x ≤ 4
- 1 ≤ x ≤ 13
- All real numbers
4.
In a notebook, Ren draws f as the segment from (-1, 9) to (5, -3). What is the range of f⁻¹?
- All real numbers
- -3 ≤ y ≤ 9
- -1 ≤ y ≤ 5
5.
Tala draws the segment from (0, -4) to (6, 8) in pencil as the graph of f. What is the range of f⁻¹?
- 0 ≤ y ≤ 6
- All real numbers
- -4 ≤ y ≤ 8
6.
On a puzzle card, f is the segment from (-5, 6) to (3, 2). Zee needs the domain of f⁻¹. What is it?
- -5 ≤ x ≤ 3
- All real numbers
- 2 ≤ x ≤ 6
On a worksheet, f(x) = (x + 4)/3. Ari undoes f to find an input. What is f⁻¹(7)?
In a notebook, Bo has f(x) = 5 − 2x. What is f⁻¹(8)?
Esme works in pencil with f(x) = (x − 1)/5. What is f⁻¹(-2)?
On a puzzle card, f(x) = 7 − 3x. Jun needs f⁻¹(-4). What is it?

Inverse functions from tables and graphs. Every version has 10 questions, and the answer key prints on the second page.

Standard: F-BF.B.4c (+)

inverse f⁻¹: The function that undoes f: it swaps inputs and outputs.

f⁻¹(5): The input of f whose output is 5. Not 1 over f.

one-to-one: No output comes from two different inputs.

horizontal line test: No sideways line crosses the graph twice, so f has an inverse.

the line y = x: The mirror line between a graph and its inverse.

Your child worked out f of the number instead of f⁻¹. f⁻¹(5) asks which input gives the output 5.

Your child read f⁻¹ as 1 over f. The small -1 means "undo f", not a reciprocal.

Your child flipped the point over the x-axis instead of over the line y = x.

Ask: is 5 an input or an output here?

Ask: which input of f gives this output?

Ask: what happens to the two numbers when you mirror over y = x?

What is the most common mistake with inverse functions from tables and graphs?

Your child worked out f of the number instead of f⁻¹. f⁻¹(5) asks which input gives the output 5.

How can I help my child with inverse functions from tables and graphs?

Ask: is 5 an input or an output here?

Are these 11th grade math worksheets free to print?

Yes. All 6 printable versions at each level are free to print, with the answer key, and no account is needed.

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