Question

The table below represents a linear function f(x) and the equation represents a function (x)f(x)-1-12g(x)09(x) = 2x + 610Part 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)I

Answer 1

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

(b)g(x) has a greater y-intercept.

Step-by-step explanation:

Part A

From the table of f(x), we have the pairs:

(-1,-12),(0,-6) and (1,0).

First, we find the slope of f(x).

`\begin{gathered} \text{Slope}=\frac{Change\text{ in y-axis}}{Change\text{ in x-axis}} \\ =(-6-0)/(0-1) \\ =-(6)/(-1) \\ =6 \end{gathered}`

Given the function g(x) defined as follows:

`g(x)=2x+6`

Comparing g(x) with the slope-intercept form (y=mx+b), the slope of g(x) is m=2.

Sentence: The slope of f(x) is greater than the slope of g(x).

Part B

The y-intercept is the point in a function where x=0.

In f(x), When x=0, f(x)=-6

• The y-intercept of f(x) is -6.

Comparing g(x) with the slope-intercept form (y=mx+b), the y-intercept of g(x), b=6.

Therefore, g(x) has a greater y-intercept.