Question

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

graph going through negative 1, negative 1 and negative 4, negative 1

x g(x)
4 | 9
6 | 13
8 | 17

A) The function g(x) has a higher y-intercept.
B) The function f(x) has a higher y-intercept.
C) They both have the same y-intercept.
D) The relationship between y-intercepts cannot be determined.

Answer 1

Hello!

The answer is:

The correct option is:

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

Why?

To solve the problem, we need to find the y-intercept of the g(x) function, and then, compare to the y-intercept of the f(x) function which is equal to -1 (we can see it on the picture).

Also, we need to remember the slope-interception form of the line:

$y=mx+b$

So,

Finding the y-intercept of the g(x) function, we have:

Calculating the slope of the function, using the first two points (4,9) and (6,13), we have:

$m=\frac{y_2-y_1}{x_2-x_1}\\\\m=\frac{13-9}{6-4}=\frac{4}{2}=2$

Now,

Calculating the value of "b", we have:

Using the first point (4,9), the slope of the function, and the slope-intercept form of the function, we have:

$y=mx+b$

$y=2x+b$

$9=2*(4)+b$

$9=8+b$

$9-8=b$

$b=1$

So, the equation of the line will be:

$y=2x+1$

We know that "b" represents the y-intercept, so, the function g(x) has its y-intercept at y equal to 1.

Comparing, we have that the function f(x) has a y-intercept located at y equal to "-1" and the g(x) function has a y-intercept located at y equal to "1".

Hence, the correct option is:

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

Have a nice day!