Answered

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.

Verified Answer :

calculista

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.

Jacquelinebramirez31

Answer:

B

Step-by-step explanation:

I just took the test and its correct!

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