Question

The table below represents a linear function f(x) and the equation represents a function g(x):

x f(x)
−1 −12
0 −6
1 0
g(x)

g(x) = 2x + 6


Part A: Write a sentence to compare the slope of the two functions and show the steps you used to determine the slope of f(x) and g(x).
Part B: Which function has a greater y-intercept? Justify your answer.

Answer 1

Answer:

Part A) The slope of the function f(x) is greater than the slope of the function g(x) (see the explanation)

Part B) Function g(x) has a greater y-intercept than the function f(x)  (see the explanation)

Step-by-step explanation:

Part A)

step 1

Find the slope of function f(x)

Find the slope m

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

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

take the points

(0,-6) and (1,0)

substitute in the formula

$m=\frac{0+6}{1-0}$

$m=\frac{6}{1}=6$

step 2

Find the slope of function g(x)

we have

$g(x)=2x+6$

This is the equation of the line in slope intercept form

$y=mx+b$

where

m is the slope

b is the intercept

In this problem we have

$m=2\\b=6$

step 3

Compare the slopes

The slope of f(x) is m=6

The slope of g(x) is m=2

therefore

The slope of the function f(x) is greater than the slope of the function g(x)

Part B)  Which function has a greater y-intercept?

we know that

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

step 1

Determine the y-intercept of the function f(x)

Looking at the data in the table

For x=0, f(x)=-6

therefore

The y-intercept of f(x) is -6

step 2

Determine the y-intercept of the function g(x)

we have

$g(x)=2x+6$

The y-intercept of the function g(x) is 6 (see part A)

Compare the y-intercept

6 > -6

therefore

Function g(x) has a greater y-intercept than the function f(x)