Question

Compare the functions shown below:

Which function has the greatest y-intercept?
See picture:

a. f(x)
b. g(x)
c. h(x)
d. All three functions have the same y-intercept.

Answer 1

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
`f(x)=4x+5`

To determine the y - intercept let us substitute x = 0 in the function.

Thus, we have;

`f(x)=4(0)+5`

`f(x)=5`

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
`h(x)=3 \sin (2 x+\pi)-2`

To determine the y - intercept, let us substitute x = 0 in the function.

Thus, we have;

`h(x)=3 \sin (2 (0)+\pi)-2`

`h(x)=3 \sin \pi -2`

`h(x)=3(0)-2`

`h(x)=-2`

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.