Question

functions g and h are graphed. find lim(x→ - 2)(g(x)h(x)).

Explanation:

Step1: Recall limit - product rule

The limit of a product of two functions is the product of their limits, i.e., $\lim_{x
ightarrow a}(f(x)g(x))=\lim_{x
ightarrow a}f(x)\cdot\lim_{x
ightarrow a}g(x)$ when both $\lim_{x
ightarrow a}f(x)$ and $\lim_{x
ightarrow a}g(x)$ exist. So, $\lim_{x
ightarrow - 2}(g(x)h(x))=\lim_{x
ightarrow - 2}g(x)\cdot\lim_{x
ightarrow - 2}h(x)$.

Step2: Find $\lim_{x

ightarrow - 2}g(x)$
As $x$ approaches $-2$ from both the left - hand side and the right - hand side, the value of $g(x)$ approaches $4$. So, $\lim_{x
ightarrow - 2}g(x)=4$.

Step3: Find $\lim_{x

ightarrow - 2}h(x)$
As $x$ approaches $-2$ from both the left - hand side and the right - hand side, the value of $h(x)$ approaches $2$. So, $\lim_{x
ightarrow - 2}h(x)=2$.

Step4: Calculate the product of the limits

$\lim_{x
ightarrow - 2}(g(x)h(x))=\lim_{x
ightarrow - 2}g(x)\cdot\lim_{x
ightarrow - 2}h(x)=4\times2 = 8$.

Answer:

$8$