Problem 9

Explanation

We verify each statement based on the functions provided in the graph: Exponential function: $y = 2^x - 2$ Linear function: $y = -2x + 4$

Checking Point A

Point $A$ is the y-intercept of the exponential curve ($x=0$).

So, $A(0, -1)$. Statement $(1)$ is TRUE.

Checking Point B

Point $B$ is the x-intercept of the exponential curve ($y=0$).

So, $B(1, 0)$. Statement $(2)$ is TRUE.

Checking Point C

Point $C$ is the x-intercept of the linear line ($y=0$).

So, $C(2, 0)$. Statement $(3)$ is TRUE.

Checking Point D

Point $D$ is the intersection point or a point on the line. The statement claims $D(2, 2)$. If we test coordinate $(2, 2)$ into the line equation $y = -2x + 4$:

The result is $y = 0$, not $2$. Thus, point $(2, 2)$ does not lie on the line $y = -2x + 4$. Statement $(4)$ is FALSE.

Conclusion: Statements $(1)$, $(2)$, and $(3)$ are correct.