Question

Compare the functions shown below:

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.