1. The problem asks us to compare the intercepts of two functions: $a(x) = -x^3 + 8$ and function $b$ represented by the given graph. 2. First, find the intercepts of function $a(x)$: - The y-intercept occurs when $x=0$: $$a(0) = -0^3 + 8 = 8$$ So, the y-intercept of $a$ is $(0, 8)$. - The x-intercept(s) occur when $a(x) = 0$: $$-x^3 + 8 = 0 \implies -x^3 = -8 \implies x^3 = 8 \implies x = 2$$ So, the x-intercept of $a$ is $(2, 0)$. 3. From the graph description of function $b$: - The y-intercept is at $(0, 8)$. - The x-intercept is near $(-2, 0)$. 4. Compare the intercepts: - Y-intercepts: $a$ and $b$ both have y-intercept $8$, so they are equal. - X-intercepts: $a$ has x-intercept at $2$, $b$ has x-intercept near $-2$. Since $2 > -2$, the x-intercept of $b$ is less than that of $a$. 5. Therefore, the correct statement is: **C. The y-intercept of b is equal to the y-intercept of a.**