Answer:
The y-intercept of functions f(x), g(x) and h(x) are 2,-3 and 3 respectively. Therefore the function h(x) has the greatest y-intercept.
Step-by-step explanation:
The given function is
[tex]f(x)=-3x+2[/tex]
Substitute x=0, to find the y-intercept of the function.
[tex]f(0)=-3(0)+2[/tex]
[tex]f(0)=0+2[/tex]
[tex]f(0)=2[/tex]
The y-intercept of the function f(x) is 2.
From the given graph it is clear that the graph of g(x) intersect the y-axis at y=-3.
Therefore the y-intercept of the function g(x) is -3.
The given function is
[tex]h(x)=4\sin (2x+\pi)+3[/tex]
Substitute x=0, to find the y-intercept of the function.
[tex]h(0)=4\sin (2(0)+\pi)+3[/tex]
[tex]h(0)=4\sin (0+\pi)+3[/tex]
[tex]h(0)=4\sin (\pi)+3[/tex]
[tex]h(0)=4(0)+3[/tex]
[tex]h(0)=3[/tex]
The y-intercept of the function h(x) is 3.
The y-intercept of functions f(x), g(x) and h(x) are 2,-3 and 3 respectively. Therefore the function h(x) has the greatest y-intercept.
