review the graph of function f(x). what are lim f(x) and lim f(x), if they exist? x→0⁻ x→0⁺ o lim f(x)=1 and…

Explanation:

Step1: Determine the left-hand limit $\lim_{x \to 0^-} f(x)$.

As $x$ approaches $0$ from the left side (values of $x < 0$), the graph of $f(x)$ (the blue curve) approaches the y-value of $1$. $$ \lim_{x \to 0^-} f(x) = 1 $$

Step2: Determine the right-hand limit $\lim_{x \to 0^+} f(x)$.

As $x$ approaches $0$ from the right side (values of $x > 0$), the graph of $f(x)$ (the red curve) approaches the y-value of $0$. $$ \lim_{x \to 0^+} f(x) = 0 $$

Answer:

$\lim_{x \to 0^-} f(x) = 1$ and $\lim_{x \to 0^+} f(x) = 0$