Question

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)

Answer 1

Part A:

To find the slope of f(x), use the following formula to find the slope:

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

Choose any two points from the table. We'll use (-1, -6) and (1, 0):

`(0 - (-6))/(1 - (-1)) = (6)/(2) = 3`

The slope of f(x) is 3.

g(x) uses slope intercept form, which uses the following formula:

`y = mx + b`

m is the slope, and b is the y-intercept of the function.

g(x) is equal to 4x - 5. The coefficient for x is 4, which is the slope of the function. The slope is 4.

Compare the two slopes:

`\text{slope of f(x) = 3}`

`\text{slope of g(x) = 4}`

`3 < 4`

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

Part B:

The y-intercept is found when x is equal to 0.

f(x) already has a value for when x = 0: the y-value is -3.

g(x)'s y-intercept is found by the value of b in the function. The value of b in this function is -5.

Compare the two y-intercepts:

`\text{y-intercept of f(x) = -3}`

`\text{y-intercept of g(x) = -5}`

`-3 > -5`

f(x) has the greater y-intercept.