Inverse functions from tables and graphs

Answer Key - Grade 11 Math Worksheet - Building Confidence

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

1. Read this first

   Table of f

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

2. 1.

   Kira's worksheet has a table of f. The inverse swaps the input and output columns. What is f⁻¹(-2)?

   2
3. 2.

   Milo uses the table of f, working in pencil. f⁻¹ undoes f. What is f⁻¹(5)?

   -3
4. 3.

   On a puzzle card, Noah sees the table of f. The table of f⁻¹ has the columns swapped. What is f⁻¹(6)?

   3
5. 4.

   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?

   (8, 3)
6. 5.

   In a notebook, Ren notes that (-2, 5) is on the graph of f. Reflecting over the line y = x gives f⁻¹. Which point is on the graph of f⁻¹?

   (5, -2)
7. 6.

   Tala draws the line y = x in pencil and marks (4, -7) on f. Which point is on the graph of f⁻¹?

   (-7, 4)
8. 7.

   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?

   (-1, -6)

9. Table of f

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

10. 8.

    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 output 3 comes from both -1 and 1.
    • No: the outputs of f are not in order.
11. 9.

    In a notebook, Bo has the table of f. Does f have an inverse function?

    • No: the outputs of f are not in order.
    • Yes: each output of f comes from just one input.
    • No: some outputs of f are negative, which blocks an inverse.
12. 10.

    Esme checks the table of f in pencil. Is the swapped table, f⁻¹, a function?

    • No: the outputs of f are not in order.
    • No: the output 8 comes from both 2 and 4.
    • Yes: each input of f has just one output.