Question

Below are two different functions, f(x) and g(x). What can be determined about their slopes? f(x) = 2x + 3 The function g of x going through 1 on the x axis and 1, 4

Answer 1

because g(x) passes from 1,0 to 1,4, we can say that it has a slope of 0. f(x) has a slope of 2. 

Answer 2

The slope of the function f(x) is 2 and the slope of g(x) is ∞. The slope of g(x) is greater than slope of f(x).

Explanation:

The given function is

`f(x)=2x+3` .... (1)

The slope intercept form of a line is

`y=mx+b` .... (2)

Where, m is slope and b is y-intercept.

From (1) and (2), we get

`m=2,b=3`

It means slope of the function f(x) is 2 and y-intercept is 3.

The function g(x) going through 1 on the x axis and (1, 4). It means it passes through the point (1,0) and (1,4).

The slope of g(x) is

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

`m=(4-0)/(1-1)`

`m=\infty`

The slope of g(x) is ∞.

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