Question

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

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

$0=-2x+1$

$2x=1$

$x=\dfrac{1}{2}$

$x=0.5$

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: