Question

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

Answer 1

F(x) = 4x-1, so the y-intercept is 4(0)-1 = -1
g(x) = x+2, so the y-intercept is (0)+2= 2
(B) The function g(x) has a higher y-intercept.

Answer 2

we have that

$f(x)=4x-1$

In the table

Let

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

Step $1$

Find the equation of the line of g(x)

Find the slope AB

slope m is equal to

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

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

$m=1$

with the slope m and the point $A(1,3)$ find the equation of the line

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

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

$y=x-1+3$

$y=x+2$

$g(x)=x+2$

Step $2$

Find the y-intercept of f(x) and g(x)

we know that

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

$f(x)=4x-1$

for $x=0$

$f(x)=4*0-1$

$f(x)=-1$

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

$g(x)=x+2$

for $x=0$

$g(x)=0+2$

$g(x)=2$

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