Question

The table below represents a linear function f(x), and the equation represents a function g(x): X) -1, 0, 1 F(x) -5, -1, 3 G(x)=4x+3

Part A. Write a sentence to compare the slope of the two functions and shows the steps you used to determine the slope of f(x) and g(x)

Part B which functions has greater y-intercept. Justify

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Answer 1

(a) g(x) has a greater slope

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

Explanation:

Given

`x \to -1,0,1`

`f(x) \to -5,-1,3`

`g(x) = 4x + 3`

Solving (a): Compare the slopes

Slope (m) is calculated as:

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

So, for f(x), we have:

`m =(-1- 0)/(-5- -1)`

`m =(-1)/(-4)`

`m =(1)/(4)`

For g(x), we have:

Assume
`g(x) = mx + c` then the slope is m

Compare the above to
`g(x) = 4x + 3`

Then the slope of g(x) is 4

g(x) has a greater slope

Solving (b): Function with greater y intercept

Here we set
`x= 0`

From the table of f(x)

`f(x) = -1` when
`x = 0`

From
`g(x) = 4x + 3`

`g(0) = 4 * 0 + 3`

`g(0) = 3`

Hence:

g(x) has a greater y intercept