Question

evaluate the function $f(x) = \frac{x}{|x|}$ at the given values of the independent variable and simplify.

a. $f(6)$

b. $f(-6)$

c. $f(r^2)$

a. $f(6) = \square$ (simplify your answer)

Explanation:

Step1: Recall the function definition

The function is \( f(x) = \frac{x}{|x|} \). For a positive number \( x \), the absolute value \( |x| = x \), so we can substitute \( x = 6 \) into the function.

Step2: Substitute \( x = 6 \) into the function

Substitute \( x = 6 \) into \( f(x) = \frac{x}{|x|} \). Since \( |6| = 6 \), we have \( f(6)=\frac{6}{|6|}=\frac{6}{6} \).

Step3: Simplify the fraction

Simplify \( \frac{6}{6} \), which equals \( 1 \).

Answer:

\( 1 \)