Question

use the graph of f(x) shown here to find each of the following limits. use ∞ to indicate that f(x) is increasing without bound, and use -∞ to indicate that f(x) is decreasing without bound.
lim f(x) lim f(x) lim f(x) lim f(x)
x→ - 4⁻ x→ - 4⁺ x→4⁻ x→4⁺
lim f(x)=
x→ - 4⁻

Explanation:

Step1: Analyze left - hand limit as x approaches - 4

We look at the graph and see the behavior of the function as x approaches - 4 from the left side (values of x less than - 4 getting closer to - 4).

Step2: Determine the trend

If the graph is going up without bound as x approaches - 4 from the left, the limit is $\infty$. If it's going down without bound, the limit is $-\infty$.
(Note: Since the graph is not provided here, we can't give a specific numerical answer. But the general process is as above. If the graph shows the function increasing without bound as x approaches - 4 from the left, the limit is $\infty$; if it shows the function decreasing without bound, the limit is $-\infty$)

Answer:

(The answer depends on the actual graph. If the function increases without bound as x approaches - 4 from the left, the answer is $\infty$. If it decreases without bound, the answer is $-\infty$)