Question

determine the y - intercept of the following rational function $f(x)=\frac{x - 5}{4x - 20}$
$\left(\frac{1}{4},0\
ight)$
$\left(0,\frac{1}{4}\
ight)$
$(0,5)$
$(5,0)$

Explanation:

Step1: Recall y - intercept formula

The y - intercept of a function $y = f(x)$ is found by setting $x = 0$.

Step2: Substitute $x = 0$ into the function

Substitute $x=0$ into $f(x)=\frac{x - 5}{4x - 20}$, we get $f(0)=\frac{0 - 5}{4\times0 - 20}=\frac{-5}{-20}$.

Step3: Simplify the fraction

$\frac{-5}{-20}=\frac{1}{4}$. The y - intercept is a point of the form $(0,y)$, so the y - intercept is $(0,\frac{1}{4})$.

Answer:

$(0,\frac{1}{4})$