Answer:
Function h(x)
Step-by-step explanation:
Given functions:
[tex]f(x)=-3x-5\\\\\textsf{Graph of function $g(x)$ (attached)}\\\\h(x)=2\cos(2x-\pi)+4[/tex]
The y-intercept of a function is the point at which the graph intersects the y-axis, represented by the coordinate (0, y). Therefore, to find the y-intercept of a function, substitute x = 0 into the function.
Determine the y-intercept of function f(x):
[tex]f(0)=-3(0)-5\\\\f(0)=0-5\\\\f(0)=-5[/tex]
Determine the y-intercept of function h(x):
[tex]h(0)=2\cos(2(0)-\pi)+4\\\\h(0)=2\cos(0-\pi)+4\\\\h(0)=2(-1)+4\\\\h(0)=-2+4\\\\h(0)=2[/tex]
From observation of the graph of function g(x), the function intersects the y-axis at (0, -3). Therefore, g(0) = -3.
So, the function that has the greatest y-intercept (the greatest value of the function at x = 0) is function h(x).
