Question

The table represents the linear function f(x), and the equation represents the linear function g(x). Compare the y-intercepts and slopes of the linear functions f(x) and g(x) and choose the answer that best describes them. x f(x) 0 1 2 9 4 17 g(x) = 3x + 1

Answer 1

Answer:

The y-intercepts of both functions are the same and the function f(x) has a greater slope than the function g(x)

Step-by-step explanation:

we know that

The formula to calculate the slope between two points is equal to

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

step 1

Determine the slope of the function f(x)

take two points from the table

(0,1) and (2,9)

substitute in the formula

$m=\frac{9-1}{2-0}$

$m=\frac{8}{2}$

$m_1=4$

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

In this problem the point (0,1) is the y-intercept

so

$b_1=1$

step 2

Determine the slope of the function g(x)

we have

$g(x)=3x+1$

This is the equation of the line in slope intercept form

$y=mx+b$

where

m is the slope

b is the y-intercept

so

In this problem

$m_2=3$

$b_2=1$

step 3

Compare the y-intercepts and slopes

$b_1=b_2\\m_1 > m_2$

The y-intercepts of both functions are the same and the function f(x) has a greater slope than the function g(x)