Question

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

x f(x)
−1 −5
0 −1
1 3


g(x)

g(x) = 2x − 7

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

Part A:

The function f(x) has a greater slope than function g(x).

Part B:

The function f(x) has a greater y-intercept than function g(x).

Explanation:

`\text{The slope-intercept form of an equation of a line:}\\\\y=mx+b\\\\m-slope\\b-y-intercept\to(0,\ b)\\\\\text{The formula of a slope:}\\\\m=(y_2-y_1)/(x_2-x_1)\\\\=============================`

`f(x):\\\\given:\ (-1,\ -5),\ (0,\ -1),\ (1,\ 3)\\\\m=(3-(-5))/(1-(-1))=(8)/(2)=4\\\\(0,\ -1)\to b=-1\\\\f(x)=4x-1\\\\---------------------------\\\\g(x)=2x-7\to m=2,\ b=-7`

Answer 2

Part A: The slope of F(x) is greater than the slope of g(x)

Part B: The Y-intercept of f(x) is greater than that of g(x)

Explanation:

To calculate the slope on f(x) we just have to take two points from the table and use the formula for slope:

`m=(y^(2) -y^(1) )/(x^(2)- x^(1) )`

Now the points to use will be:

P1:(0,-1)

P2:(1,3)

Now we just put this values into the formula:

`m=(y^(2) -y^(1) )/(x^(2)- x^(1) )`

`m=(3-(-1) )/(1- (0)) }`

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

Now to know the slope of g(x) we just have to remember that in the function form y=mx+c the "m" represents the slope, so if g(x)=2x-7 the slope would be "2".

Now we know that f(x) has a greater slope.

To know the greater Y intercept we just take the point in the table where x is "0" since it´s where the Y intercepts with the Y axis, and in f(x) that point is (0,-1), now in g(x) we just evaluate the function to x=0.

`g(x)=2x-7\\g(x)=2(0)-7\\g(x)=-7`

The Y intercept in g(x) would be in (0,-7), since -1 is greater than -7, we can say that f(x) has the greatest Y-intercept.