Question

For the linear function f(x) = -2x+1 , find the following

a. Slope and Y-intercept.
b. Is the function increasing, decreasing, or constant, justify your answer.
c. Graph the function, label x, and y-intercepts.

Answer 1

Given:

The function is:

`f(x)=-2x+1`

To find:

a. Slope and Y-intercept.

b. Is the function increasing, decreasing, or constant, justify your answer.

c. Graph the function, label x, and y-intercepts.

Solution:

a. We have,

`f(x)=-2x+1` ...(i)

The slope intercept form of a line is:

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

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

On comparing (i) and (ii), we get

`m=-2,b=1`

Therefore, the slope of the line is -2 and the y-intercept is 1.

b. If the slope of a linear function is negative, then the function is decreasing.

If the slope of a linear function is positive, then the function is increasing.

If the slope of a linear function is 0, then the function is constant.

The slope of the linear function is negative.

Therefore, the function is decreasing.

c. We have,

`f(x)=-2x+1`

At
`x=0`, we get

`f(0)=-2(0)+1`

`f(0)=1`

So, the y-intercept is at (0,1).

At
`f(x)=0`, we get

`0=-2x+1`

`2x=1`

`x=(1)/(2)`

`x=0.5`

So, the x-intercept is at
`\left(0.5,0\right)`.

Plot the points
`(0,1), \left(0.5,0\right)` and connect them by a straight line as shown below: