Question

Below are two different functions, f(x) and g(x). What can be determined about their y-intercepts?

Answer 1

Hello!

The answer is:

C) They both have the same y-intercept.

Why?

In order to find the correct option, we need to find the equation of the function g(x), and then, compare its y-intercept with the y-intercept of the f(x) function.

So,

- Finding the equation of the g(x):

Calculating the slope of the function, using the first two points (-1,8) and (1,0), we have:

$m=\frac{y_2-y_1}{x_2-x_1}\\\\m=\frac{0-8}{1-(-1)}=\frac{-8}{2}=-4$

Now, calculating the value of "b" using the first point (-1,8)  and the slope of the function, we have:

$y=mx+b$

$y=-x+b$

$8=-4(-1)+b$

$b=4$

So, the equation of g(x) is:

$y=-4x+4$

- Comparing the y-intercepts of f(x) and g(x):

Finding the y-intercept of f(x),  by making "x" equal to 0, we have:

$y=x+4\\\\y=4$

We have that the function f(x) has its y-intercept at "y" equal to 4.

Finding the y-intercept of g(x), by making "x" equal to 0, we have:

$y=-4x+4$

$y=-4*(0)+4$

$y=4$

We have that the function g(x) has its y-intercept at "y" equal to 4.

Hence, we have that both functions have their y-intercepts at the same point, so, the correct option is:

C) They both have the same y-intercept.

Have a nice day!

Answer 2

Answer:

D) The relationship between y-intercepts cannot be determined.

Step-by-step explanation:

We have been given two different functions f(x) and g(x). Now we need to find about what can be determined about their y-intercepts. Then match with the correct choice from the given choices:

A) The function f(x) has a higher y-intercept.

B) The function g(x) has a higher y-intercept.

C) They both have the same y-intercept.

D) The relationship between y-intercepts cannot be determined.

We know that y-intercept is the y of function value when x=0.

In the table of g(x), we don't see any point that has x=0

So we can't find the y-intercept for g(x)

Hence correct choice is :

D) The relationship between y-intercepts cannot be determined.