Question

Below are two different functions, f(x) and g(x). What can be determined about their y-intercepts? f(x) = 4x − 1

x g(x)
1 3
4 6
7 9
answers:
AThe function f(x) has a higher y-intercept.
B The function g(x) has a higher y-intercept.
CThey both have the same y-intercept.
D The relationship between y-intercepts cannot be determined.

Answer 1

B

Explanation:

I just took the test and its correct!

Answer 2

we know that

The y-intercept is the value of the function when the value of x is equal to zero

Step
`1`

Find the y-intercept of f(x)

`f(x)=4x-1`

for
`x=0`

`f(0)=4*0-1`

`f(0)=-1`

the y-intercept of f(x) is equal to
`-1`

Step
`2`

Find the equation of the line g(x)

Let

`A(1,3)\\B(4,6)\\C(7,9)`

Find the slope AB

the slope m is equal to

`m=((y2-y1))/((x2-x1))`

substitute the values

`m=((6-3))/((4-1))`

`m=1`

with the slope and the point A find the equation of the line

`y-y1=m(x-x1)`

`y-3=1*(x-1)`

`y=x-1+3`

`y=x+2`

therefore

the function g(x) is equal to

`g(x)=x+2`

Step
`3`

Find the y-intercept of g(x)

`g(x)=x+2`

for
`x=0`

`g(0)=0+2`

`g(0)=2`

the y-intercept of g(x) is equal to
`2`

therefore

the answer is the option

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