Question

the table above shows selected values of a continuous function f. for 0 ≤ x ≤ 13, what is the fewest possible number of times f(x)=4?
a one
b two
c three
d four

Explanation:

Step1: Analyze function values

We have $f(0)=3$, $f(4) = 4.5$, $f(6)=3$, $f(8)=2.5$, $f(13)=4.4$. Since $f(x)$ is continuous.

Step2: Apply Intermediate - Value Theorem

Between $x = 0$ and $x = 4$, as $f(x)$ goes from $3$ to $4.5$, it must cross $y = 4$ at least once. Between $x=6$ and $x = 13$, as $f(x)$ goes from $3$ to $4.4$, it must cross $y = 4$ at least once.

Answer:

B. two