Find all intercepts of the following function.
$g ( x ) = \frac { - 1 } { x + 3 }$
A)x-intercept: $\left( - \frac { 1 } { 3 } , 0 \right)$
B)y-intercept: $\left( 0 , - \frac { 1 } { 3 } \right)$
C)x-intercept: $\left( - \frac { 1 } { 3 } , 0 \right)$ and y-intercept: $\left( 0 , - \frac { 1 } { 3 } \right)$
D)x-intercept: $\left( \frac { 1 } { 3 } , 0 \right)$
E)y-intercept: $\left( 0 , \frac { 1 } { 3 } \right)$

Question

Find all intercepts of the following function. 
 $g ( x ) = \frac { - 1 } { x + 3 }$  
A)x-intercept: $\left( - \frac { 1 } { 3 } , 0 \right)$
B)y-intercept: $\left( 0 , - \frac { 1 } { 3 } \right)$
C)x-intercept: $\left( - \frac { 1 } { 3 } , 0 \right)$ and y-intercept: $\left( 0 , - \frac { 1 } { 3 } \right)$
D)x-intercept: $\left( \frac { 1 } { 3 } , 0 \right)$
E)y-intercept: $\left( 0 , \frac { 1 } { 3 } \right)$

Quizplus · Accepted Answer

To find the y-intercept, set $x = 0$: $g(0) = \frac{-1}{0+3} = -\frac{1}{3}$, so the y-intercept is $\left(0, -\frac{1}{3}\right)$. For the x-intercept, set $g(x) = 0$, but there is no value of $x$ that makes $\frac{-1}{x+3} = 0$, so there is no x-intercept.

Find All Intercepts of the Following Function g(x)=−1x+3g ( x ) = \frac { - 1 } { x + 3 }g(x)=x+3−1​

Find All Intercepts of the Following Function $g ( x ) = \frac { - 1 } { x + 3 }$