Answer
Please see the graph.
Work Step by Step
$f(x)=3/4*abs(x+1)−4$
Since the coefficient of the function is positive, the graph opens upward. We have the vertex of the graph when $abs (x+1)$ is at its lowest point. Thus, at the vertex, x=-1.
$x=-1$
$f(x)=3/4*abs(x+1)−4$
$f(-1)=3/4*abs(-1+1)−4$
$f(-1)=3/4*abs(0)−4$
$f(-1)=3/4*0−4$
$f(-1)=0-4$
$f(-1)=-4$
The vertex is at $(-1,−4)$. Since this point is below the x-axis, there are x-intercepts.
$f(x)=3/4*abs(x+1)−4$
$0=3/4*abs(x+1)−4$
$0+4=3/4*abs(x+1)−4+4$
$4 = 3/4*abs(x+1)$
$4*4/3 = 3/4*4/3*abs(x+1)$
$16/3 = abs (x+1)$
$16/3 = abs (x+1)$
$16/3 = x+1$
$16/3 -1 =x+1-1$
$13/3 = x$
$-16/3 = abs (x+1)$
$-16/3 = x+1$
$-16/3 - 1 =x+1-1$
$-19/3 = x$
We have the x-intercepts of $(-19/3, 0)$ and $(13/3, 0)$.
