Answer:
The function f(x) has the greatest y-intercept. Option 1 is correct.
Step-by-step explanation:
The first function is
[tex]f(x)=4x+5[/tex]
Substitute x=0 in the given function, to find the y-intercept.
[tex]f(0)=4(0)+5=5[/tex]
The y-intercept of f(x) is 5.
From the given graph it is clear that the y-intercept of g(x) is 2.
The third function is
[tex]h(x)=3\sin (2x+\pi)-2[/tex]
Substitute x=0 in the given function, to find the y-intercept.
[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]
The y-intercept of h(x) is -2.
[tex]5>2>-2[/tex]
Therefore the function f(x) has the greatest y-intercept. Option 1 is correct.
