Question

Please helpppp now 99 points

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


x f(x)
−1 −15
0 −10
1 −5
g(x)

g(x) = 2x + 8


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). (6 points)

Part B: Which function has a greater y-intercept? Justify your answer. (4 points)

Answer 1

Part A:

In order to find the slope of
`f(x)` we can use the formula:

`m=(y_2-y_1)/(x_2-x_1)`

So, using first two pairs from the given table we have:

`m=(-10-(-15))/(0-(-1))=(-10+15)/(1)=(5)/(1)=5`

Every linear function has the following general look:

`y=mx+b`, where
`m` is the slope of the function.

Applying that general look to our function
`g(x)` we see that it's slope equals 2.

So, we can say that value of
`f(x)` is growing two and half more times faster then value of
`g(x)` as their slopes' ratio is 5:2.

Part B:
The y-intercept of function is it's value in case x is equal 0.
Using the given table we find that the y-intercept of
`f(x)=-10`

As for
`g(x)`, let's substitute x value with 0 and solve the equation:

`g(x)=2\cdot0+8=8`

So, the function
`g(x)` has greater y-intercept then function
`f(x)`.