Question

The table below represents a linear function f(x) and the equation represents a function g(x): x f(x) −1 −7 0 −1 1 5 g(x) g(x) = 5x − 4 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

Answer:

Part A: The slope of the function f( x ) is one greater than the slope of the function g( x ), f( x ) having 6 as the slope, and g( x ) having 5,

Part B: The function f( x ) has a greater y - intercept.

Step-by-step explanation:

I believe you meant the table to be the following,

x | f(x)

- 1 - 7

0  - 1  

1    5 .... if that is so, we can determine the slope in two ways through the change in the y - axis over the change in the x - axis. f( x ), otherwise known to function of x, is also known as the y - value. Therefore, if f( x ) changes by an additional 6, and x changes by an additional 1, we know that the slope should be $\frac{6}{1}$, or 6.

Now the function " $g( x ) = 5x - 4$ " is in point - slope form, so we know that the slope is coefficient of x, in this case 5. We can compare the slopes by the following claim -

Part A Solution: The slope of the function f( x ) is one greater than the slope of the function g( x ), f( x ) having 6 as the slope, and g( x ) having 5.

To determine the y - intercept of the function f( x ), we can check the point ( 0, - 1 ). When x is 0, y is - 1, and therefore the y - intercept should be - 1. At the same time the function g( x ) has a y - intercept of - 4, as it is in the form g( x ) = m $*$ x + b, where b = y - intercept. Part B Solution: Thus, the function f( x ) has a greater y - intercept.