Questions: Given the function C(r)=(r-4)(r+7)(r-3) its C-intercept is its r-intercepts are

Solution Steps

To find the $C$-intercept, evaluate the function at $r = 0$. For the $r$-intercepts, set the function equal to zero and solve for $r$.

To find the $C$-intercept, we evaluate the function $C(r)$ at $r = 0$: $$C(0) = (0 - 4)(0 + 7)(0 - 3) = (-4)(7)(-3) = 84$$ Thus, the $C$-intercept is $84$.

To find the $r$-intercepts, we set the function $C(r)$ equal to zero: $$(r - 4)(r + 7)(r - 3) = 0$$ This gives us the solutions: $$r - 4 = 0 \quad \Rightarrow \quad r = 4$$ $$r + 7 = 0 \quad \Rightarrow \quad r = -7$$ $$r - 3 = 0 \quad \Rightarrow \quad r = 3$$ Thus, the $r$-intercepts are $-7, 3,$ and $4$.

Final Answer