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.
The answer is:
C) They both have the same y-intercept.
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:
[tex]m=\frac{y_2-y_1}{x_2-x_1}\\\\m=\frac{0-8}{1-(-1)}=\frac{-8}{2}=-4[/tex]
Now, calculating the value of "b" using the first point (-1,8) and the slope of the function, we have:
[tex]y=mx+b[/tex]
[tex]y=-x+b[/tex]
[tex]8=-4(-1)+b[/tex]
[tex]b=4[/tex]
So, the equation of g(x) is:
[tex]y=-4x+4[/tex]
- 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:
[tex]y=x+4\\\\y=4[/tex]
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:
[tex]y=-4x+4[/tex]
[tex]y=-4*(0)+4[/tex]
[tex]y=4[/tex]
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!
