Inverse functions from tables and graphs

Answer Key - Grade 11 Math Worksheet

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

1. 1.

   Kira's worksheet shows the graph of f. The inverse undoes f. What is f⁻¹(-3)?

   -2
2. 2.

   In a notebook, Luz reads the graph of f backward, from an output to its input. What is f⁻¹(-4)?

   3
3. 3.

   Milo traces the graph of f in pencil. What is f⁻¹(-1)?

   -3
4. 4.

   Pia's worksheet shows the graph of f(x) = x² − 4. Does f have an inverse function?

   • Yes: every vertical line crosses the graph at most once, so it is a function.
   • No: the line y = 5 crosses the graph at x = -3 and x = 3.
   • No: the graph is not a straight line.
5. 5.

   In a notebook, Ren sketches the graph of f(x) = x³ + 1. Does f have an inverse function?

   • No: the graph is not a straight line, so there is no inverse function.
   • No: the graph crosses the y-axis.
   • Yes: every horizontal line crosses the graph at most once.
6. 6.

   Tala draws the graph of f(x) = |x − 2| in pencil. Is there an inverse function for f?

   • Yes: every vertical line crosses the graph at most once, so f is a function.
   • No: the line y = 3 crosses the graph at x = -1 and x = 5.
   • No: the graph is not a straight line.
7. 7.

   On a puzzle card, Zee sees the graph of f(x) = 2ˣ. Does f have an inverse function?

   • No: the graph crosses the y-axis.
   • Yes: every horizontal line crosses the graph at most once.
   • No: the graph is not a straight line.
8. 8.

   On a worksheet, f(x) = 3x − 2. Ari wants the input that gives the output 10. What is f⁻¹(10)?

   4
9. 9.

   In a notebook, Bo has f(x) = 4x + 5 and undoes it. What is f⁻¹(29)?

   6
10. 10.

    On a puzzle card, f(x) = 5x − 8. Jun needs f⁻¹(22). What is it?

    6