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

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

$m=\frac{(y2-y1)}{(x2-x1)}$

substitute the values

$m=\frac{(6-3)}{(4-1)}$

$m=1$

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.

Answer 2

Answer:

B

Step-by-step explanation:

I just took the test and its correct!