Use algebra to evaluate the right-hand limit of $f(x)=\frac{|x-8|}{2 x-16}$
as $x \rightarrow 8$
.
A)1/2
B)-1/2
C)1/8
D)-1/8

Question

Use algebra to evaluate the right-hand limit of $f(x)=\frac{|x-8|}{2 x-16}$
 as $x \rightarrow 8$
 .
A)1/2
B)-1/2
C)1/8
D)-1/8

Quizplus · Accepted Answer

When evaluating the right-hand limit as $x \rightarrow 8$, we consider values of $x$ that are greater than 8. For $x > 8$, $|x-8| = x-8$, so the function simplifies to $f(x) = \frac{x-8}{2x-16}$. Factoring out the denominator gives $f(x) = \frac{x-8}{2(x-8)}$, which simplifies to $1/2$ when $x \neq 8$. Thus, the right-hand limit as $x \rightarrow 8$ is $1/2$.

Use Algebra to Evaluate the Right-Hand Limit Of f(x)=∣x−8∣2x−16f(x)=\frac{|x-8|}{2 x-16}f(x)=2x−16∣x−8∣​ As x→8x \rightarrow 8x→8

Use Algebra to Evaluate the Right-Hand Limit Of $f(x)=\frac{|x-8|}{2 x-16}$ As $x \rightarrow 8$