Provide an appropriate response.
-Suppose that a polynomial function $f$ is defined in such a way that $f ( - 4.7 ) = - 3$ and $f ( 5 ) = 1$. What conclusion does the Intermediate Value Theorem allow you to make?
A) There must be a zero between $- 3$ and 1 .
B) There must be two zeros between $- 4.7$ and 5 .
C) There must be a zero between $- 4.7$ and 5 .
D) There is not enough information to draw a conclusion about the zeros of $f$.

Question

Quizplus · Accepted Answer

The Intermediate Value Theorem states that if a function $f$ is continuous on a closed interval $[a, b]$, and $N$ is any number between $f(a)$ and $f(b)$, then there is at least one number $c$ in the interval $(a, b)$ such that $f(c) = N$. Since $f(-4.7) = -3$ and $f(5) = 1$, and the function changes sign between these two points, there must be at least one zero (where $f(c) = 0$, which is between $-3$ and $1$) in the interval $(-4.7, 5)$.

Provide an Appropriate Response fff Is Defined in Such a Way That

Provide an Appropriate Response $f$ Is Defined in Such a Way That