Question

use the graph below to determine whether the statements about the function y = f(x) are true or false. true or false: $limlimits_{x \to -3^+} f(x) = 9$ (true, false) true or false: $limlimits_{x \to 0^-} f(x) = 3$ (false, true) true or false: $limlimits_{x \to 0^-} f(x) = limlimits_{x \to 0^+} f(x)$ (false, true)

Explanation:

First Statement: $\boldsymbol{\lim_{x \to -3^+} f(x) = 9}$

Step1: Analyze right-hand limit at $x=-3$

The right-hand limit as $x \to -3^+$ looks at values of $x$ just greater than $-3$. From the graph, near $x=-3$ (right side), the function approaches $9$ (matches the blue dot/behavior).

Step1: Analyze left-hand limit at $x=0$

The left-hand limit as $x \to 0^-$ looks at values of $x$ just less than $0$. From the graph, near $x=0$ (left side), the function approaches $0$ (not $3$), so the limit is not $3$.

Step1: Find left-hand limit at $x=0$

As $x \to 0^-$, the function (left of $x=0$) approaches $0$ (from the parabola’s vertex near $y=0$).

Step2: Find right-hand limit at $x=0$

As $x \to 0^+$, the function (right of $x=0$) also approaches $0$ (same parabola behavior).

Step3: Compare the two limits

Since both $\lim_{x \to 0^-} f(x)$ and $\lim_{x \to 0^+} f(x)$ equal $0$, they are equal.

Answer:

True

Second Statement: $\boldsymbol{\lim_{x \to 0^-} f(x) = 3}$