Question

PLEASE HELP

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


x f(x)
−1 −12
0 −6
1 0
g(x)

g(x) = 2x + 6


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

QUESTION A

We can use any two points from the table to determine the slope of the linear function represented by table.

We use (0,-6) and (1,0).

We use the formula,

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

`m = (0 - - 6)/(1 - 0) = 6`

For the second function

`g(x) = 2x + 6`

This function is of the form;

`y = mx + c`

where

`m = 2`

is the slope.

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

Part B

At y-intercept , x=0.

From the table, x=0 when y=-6.

Therefore f(x) has y-intercept -6.

For

`g(x) = 2x + 6`

the y-intercept is 6.

Therefore g(x) has greater y-intercept.

Answer 2

1.the slope of the function f(x) is greater than the slope of the function g(x)

2. the y intercept in the function g(x) is the greater

Explanation:

1. plot the graph for the function f(x)

identify points in on the line, i.e (2,6) and (1,0)

find the slope of function f(x)= change in y/change in x

m=(6-0)/2-1 = 6

equation for the function f(x)= {y-6/x-2}=6

y-6=6x-12

y=6x-6

2. the equations for functions

f(x) is given by y=6x-6

g(x) is given by y=2x+6

y intercept for f(x) =- 6

y intercept for g(x)= +6

g(x) has greater y intercept.