Question

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

x f(x)
−1 −9
0 −1
1 7
g(x)

g(x) = 3x − 2


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

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

(b) f(x) has a greater y intercept

Explanation:

Given

`\begin{array}{cc}x & {f(x)} & -1&-9&0&-1&1&7 \ \end{array}`

`g(x) = 3x - 2`

Solving (a): Compare the slopes

The slope (m) of f(x) is calculated as;

`m = (f(x_2) - f(x_1))/(x_2 - x_1)`

This gives:

`m = (f(0) - f(1))/(0 - 1)`

`m = (f(0) - f(1))/(- 1)`

Substitute values for f(0) and f(1)

`m = (-1 - 7)/(- 1)`

`m = (-8)/(- 1)`

`m = 8`

The slope of g(x) can be gotten using the following comparison

`g(x) = mx + b`

`m \to slope`

So:

`g(x) = 3x -2`

`m = 3`

`m_(f(x)) > m_(g(x))`

Solving (b): Compare the y intercept

y intercept is when
`x = 0`

From the table of f(x)

`f(0) = -1`

From the equation of g(x)

`g(x) = 3x -2`

`g(0) = 3*0-2`

`g(0) =-2`

`f(0) > g(0)`