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:
[tex]f(x)=-3x-5[/tex]
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:
[tex]h(x)=2\cos\left(2x-\pi\right)+4[/tex]
To find the y-intercept, substitute x=0 into the equation:
[tex]\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}[/tex]
Hence, the y-intercept of h(x) is 2.
It follows that h(x) has the greatest y-intercept.
