Question

problems 9 - 12, use the graphs of f and g below to evaluate

1. limx→ - 2f(x)+4g(x)

limx→ - 2f(x)+4limx→ - 2g(x)
+4(-1)

Explanation:

Step1: Apply limit - sum rule

$\lim_{x
ightarrow - 2}[f(x)+4g(x)]=\lim_{x
ightarrow - 2}f(x)+4\lim_{x
ightarrow - 2}g(x)$

Step2: Determine $\lim_{x

ightarrow - 2}f(x)$ from the graph
From the graph of $y = f(x)$, as $x$ approaches $-2$, $\lim_{x
ightarrow - 2}f(x)=2$

Step3: Determine $\lim_{x

ightarrow - 2}g(x)$ (assume from graph details not shown completely but based on context)
Let's assume $\lim_{x
ightarrow - 2}g(x)=-1$

Step4: Calculate the final result

$\lim_{x
ightarrow - 2}f(x)+4\lim_{x
ightarrow - 2}g(x)=2 + 4\times(-1)=2-4=-2$

Answer:

$-2$