### Home > CALC > Chapter 2 > Lesson 2.2.2 > Problem2-71

2-71.
1. If , find: Homework Help ✎

1. f(x − 5)

2. f(2m + 3)

3. f(x + h)

4. For parts (a) and (b), explain the graphical significance of and.

What does the graph look like to the right?

What does the graph look like to the left?

Since there is a vertical asymptote at x = − 5, the limit does not exist. But we can still determine if f(x) approaches +∞, −∞ or both. We are to determine if there is agreement among the limits as x → − 5 from each side.

$\text{Test }\lim_{x\rightarrow -5^{+}}f(x)=\lim_{x\rightarrow -5^{+}}\frac{x-3}{x+5}=$

Test a point close to x = −5 but a little bit larger:

$\lim_{x\rightarrow -4.9^{+}}\frac{x-3}{x+5}=\frac{(-)}{(+)}=(-)$

Therefore, x → −5+, f(x) → −∞

$\text{Now test }\lim_{x\rightarrow -5^{-}}f(x)$

$\text{You will find }f(x)\rightarrow +\infty .$

$\text{Since }\lim_{x\rightarrow -5^{+}}f(x)\neq \lim_{x\rightarrow -5^{-}}f(x)$

$\lim_{x\rightarrow -5}f(x)\text{ does not exist.}$

Evaluate and simplify.

Refer to hint (d).

Refer to hint (d).

Refer to hints (a) and (b).