Question

Which function has the greatest y-intercept?Group of answer choicesf(x)g(x)h(x)All three functions have the same y-intercept.

Answer 1

Three functions are given. It is required to find the greatest y-intercept of the three functions.

To do this, find the y-intercept of each function and check which of them has the greatest value.

The given equation for f(x) is:

$f(x)=-3x-5$

Notice that this is a linear function in the slope-intercept form, y=mx+c.

Where m is the slope and c is the y-intercept.

Compare to the given equation; it follows that the y-intercept of f(x) is c=-5.

The y-intercept of f(x) is -5.

The graph of g(x) is given.

Recall that the y-intercept is the point where the graph of a function intersects the y axis.

Hence, the y-intercept of g(x) is -3.

The equation for h(x) is:

$h(x)=2\cos\left(2x-\pi\right)+4$

To find the y-intercept, substitute x=0 into the equation:

$\begin{gathered} h(0)=2\cos\left(2(0)-\pi\right)+4 \\ \Rightarrow h(0)=2\cos\left(0-\pi\right)+4=2\cos(-\pi\rparen+4 \\ \Rightarrow h(0)=2(-1)+4=-2+4=2 \end{gathered}$

Hence, the y-intercept of h(x) is 2.

It follows that h(x) has the greatest y-intercept.