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 - Building Confidence

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Read this first
Table of f
x f(x)
-2 7
0 4
2 -2
4 0
6 -5
Kira's worksheet has a table of f. The inverse swaps the input and output columns. What is f⁻¹(-2)?
In a notebook, Luz copies the table of f shown and swaps its two columns. What is f⁻¹(9)?
Milo uses the table of f, working in pencil. f⁻¹ undoes f. What is f⁻¹(5)?
On graph paper, Pia marks (3, 8) on the graph of f. The graph of f⁻¹ is its mirror image over y = x. Which point is on f⁻¹?
Tala draws the line y = x in pencil and marks (4, -7) on f. Which point is on the graph of f⁻¹?
On a puzzle card, (-6, -1) is on the graph of f. Zee mirrors it over y = x. Which point is on the graph of f⁻¹?
Table of f
x f(x)
-2 6
-1 3
0 2
1 3
2 6
7.
Ari's worksheet shows the table of f. Swapping the columns gives the table of f⁻¹. Is f⁻¹ a function?
- Yes: each input of f has just one output.
- No: the outputs of f are not in order.
- No: the output 3 comes from both -1 and 1.
8.
In a notebook, Bo has the table of f. Does f have an inverse function?
- No: some outputs of f are negative, which blocks an inverse.
- No: the outputs of f are not in order.
- Yes: each output of f comes from just one input.
9.
Esme checks the table of f in pencil. Is the swapped table, f⁻¹, a function?
- No: the output 8 comes from both 2 and 4.
- Yes: each input of f has just one output.
- No: the outputs of f are not in order.
10.
On a puzzle card, Jun sees the table of f. Does f have an inverse function?
- Yes: each output of f comes from just one input.
- No: some outputs of f are negative.
- No: the outputs of f are not in order from smallest to largest.

x	f(x)
-2	7
0	4
2	-2
4	0
6	-5

x	f(x)
-2	6
-1	3
0	2
1	3
2	6

11th grade Inverse functions from tables and graphs worksheet – printable — Print: 1 2 3 4 5 6

About this worksheet

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

What your child will learn

I can read f⁻¹(5) from a table or a graph of f.
I can find the point on f⁻¹ that matches a point on f.
I can tell from a table or a graph whether f has an inverse function.

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

Words to know

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.

Common mistakes

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.

What to say

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?

Questions parents ask

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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