Question

the graph of the function f is shown above. for what values of a does \\(\lim_{x \to a} f(x) = 0\\)? \\(\boldsymbol{\text{options:}}\\) \\(\boldsymbol{\text{a)}}\\) 2 only \\(\boldsymbol{\text{b)}}\\) 2 and 4 \\(\boldsymbol{\text{c)}}\\) 0 and 2 only \\(\boldsymbol{\text{d)}}\\) 0, 1, and 2

Explanation:

To determine when $\lim_{x \to a} f(x) = 0$, we check the left - hand limit and right - hand limit as $x$ approaches $a$.

• For $a = 2$: As $x$ approaches 2 from the left and the right, the function values approach 0. So $\lim_{x \to 2}f(x)=0$.
• For $a = 4$: As $x$ approaches 4 from the left and the right, the function values approach 0. So $\lim_{x \to 4}f(x)=0$.
• For $a = 0$: The left - hand limit and right - hand limit as $x$ approaches 0 do not equal 0.
• For $a = 1$: The left - hand limit and right - hand limit as $x$ approaches 1 do not equal 0.

So the values of $a$ for which $\lim_{x \to a}f(x) = 0$ are 2 and 4.

Answer:

B. 2 and 4