why is f(x) the greatest y-intercept

Find all y-intercepts:

1. For f(x): when x=0 you have that f(0)=-3·0-5=-5, then y-intercept is a point (0,-5).

2. For g(x): from the task conditions you have that g(x) is cosine function with y intercept at 0, negative 3, then y-intercept is a point (0,-3).

3. For h(x): when x=0 you have that h(0)=cos(2·0-π)+4=cos(-π)+4=-1+4=3, then y-intercept is a point (0,3).

As you can see the greatest y-intercept has function h(x).

correct choice is C.

Find all y-intercepts:

1. For f(x): when x=0 you have that f(0)=-3·0-5=-5, then y-intercept is a point (0,-5).

2. For g(x): from the task conditions you have that g(x) is cosine function with y intercept at 0, negative 3, then y-intercept is a point (0,-3).

3. For h(x): when x=0 you have that h(0)=cos(2·0-π)+4=cos(-π)+4=-1+4=3, then y-intercept is a point (0,3).

As you can see the greatest y-intercept has function h(x).

correct choice is C.

+3, 0

Step-by-step explanation:

y-intercept for f(x) is when x = 0, so it is +1, 0

y-intercept for g(x) is when x = 0, so it is +3, 0

y-intercept for h(x) is when x = 0, so it is -2, 0

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

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

Thus, we have;

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

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

Thus, we have;

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.