Given:
Given that the three functions f(x), g(x) and h(x)
We need to determine the function that has the greatest y -intercept.
The y - intercept of f(x):
The function f(x) is [tex]f(x)=4x+5[/tex]
To determine the y - intercept let us substitute x = 0 in the function.
Thus, we have;
[tex]f(x)=4(0)+5[/tex]
[tex]f(x)=5[/tex]
The y - intercept of f(x) is 5.
The y - intercept of g(x):
From the figure, the value of y when x = 0 is 2.
Thus, the y - intercept of g(x) is 2.
The y - intercept of h(x):
The function h(x) is [tex]h(x)=3 \sin (2 x+\pi)-2[/tex]
To determine the y - intercept, let us substitute x = 0 in the function.
Thus, we have;
[tex]h(x)=3 \sin (2 (0)+\pi)-2[/tex]
[tex]h(x)=3 \sin \pi -2[/tex]
[tex]h(x)=3(0)-2[/tex]
[tex]h(x)=-2[/tex]
Thus, the y - intercept of h(x) is -2.
Hence, the function that has the greatest y - intercept is f(x).
Thus, Option a is the correct answer.
