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.

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

take the points

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

substitute in the formula

step 2

Find the slope of function g(x)

we have

This is the equation of the line in slope intercept form

where

m is the slope

b is the intercept

In this problem we have

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

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)

a.) list the factors of 40.

1/2/4/5/8/10/20/40

b.) list the factors of 40 that represent the number of cans that could be on each shelf.

5

c.) how many different arrangements of cans are possible?

just one because if you put more on one shelf you will go way over 40 and the cabinet will probably break.

d.) what are the possible arrangements of the cans?

put 5 cans on each self to reach 40 cans in total.

e.) which arrangement uses all the shelves?

5 because you can put 5 cans on each shelf, and since there are 8 shelfs you are equally going to get 40 cans.