Find all intercepts for the given function. Round to the nearest tenth if necessary.
-$$f ( x ) = 5 ( x + 1 ) - 1$$
A) $x$-int: $( 1,0 )$; y-int: $( 0,1 )$
B) $x$-int: $( 1,0 )$; $y$-int: $( 0,4 )$
C) $x$-int: $( - 1,0 )$; $y$-int: $( 0,1 )$
D) $x$-int: $( - 1,0 )$; $y$-int: $( 0,4 )$

Question

Quizplus · Accepted Answer

To find the $x$-intercept, we set $f(x)=0$ and solve for $x$:

\begin{align*}
5(x+1)-1&=0\
5(x+1)&=1\
x+1&=\frac15\
x&=\frac15-1=-\frac45
\end{align*}

So the $x$-intercept is approximately $(-0.8,0)$.

To find the $y$-intercept, we set $x=0$ and calculate:

\begin{align*}
f(0)&=5(0+1)-1\
&=4
\end{align*}

So the $y$-intercept is approximately $(0,4)$.

Therefore, the best choice is D, as it correctly identifies both intercepts.

Find All Intercepts for the Given Function f(x)=5(x+1)−1f ( x ) = 5 ( x + 1 ) - 1f(x)=5(x+1)−1

Find All Intercepts for the Given Function $f ( x ) = 5 ( x + 1 ) - 1$