Question

(03.03 MC) The table below represents a linear function f(x) and the equation represents a function g(x): x f(x) −1 −6 0 −3 1 0 g(x) g(x) = 4x − 5 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) (10 points)

Answer 1

The function g(x) has a greater slope and the function f(x) has a greater y-intercept

How to compare the slopes?

The function is given as:

Function f(x)

x    f(x)

-1     -6

0     -3

1       0

g(x) = 4x - 5

The slope of f(x) is calculated using:

$m = \frac{f(1) - f(0)}{1 -0}$

This gives

$m = \frac{0 + 3}{1 -0}$

Evaluate

m = 3

By the general format of a linear equation, the slope of the function g(x) is:

m = 4

4 is greater than 3

Hence, the function g(x) has a greater slope

How to compare the y-intercepts?

This is when x = 0

For the function f(x), we have:

f(0) = -3

For the function g(x), we have:

g(0) = 5-

-3 is greater than -5

Hence, the function f(x) has a greater y-intercept

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