Question

graph the inverse of the graph shown on the same axis. is the inverse a function?

Explanation:

Step1: Identify key points of original function

Key points (x, y) on the original graph:
$(2, 0)$, $(4, 2)$, $(0, 10)$, $(7, 7)$, $(9, 9)$

Step2: Find inverse function points

Swap x and y for inverse points (y, x):
$(0, 2)$, $(2, 4)$, $(10, 0)$, $(7, 7)$, $(9, 9)$

Step3: Graph inverse and test function rule

Plot the swapped points and connect them to mirror the original graph over the line $y=x$. Check if any vertical line intersects the inverse graph more than once: the vertical line $x=7$ intersects the inverse graph at $(7,7)$ and $(7,0)$, violating the vertical line test.

Answer:

The inverse graph is the reflection of the original graph over the line $y=x$, using the points $(0, 2)$, $(2, 4)$, $(10, 0)$, $(7, 7)$, $(9, 9)$. No, the inverse is not a function.