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.

Given:

The function is:

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,

                 ...(i)

The slope intercept form of a line is:

                   ...(ii)

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

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

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,

At , we get

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

At , we get

So, the x-intercept is at .

Plot the points and connect them by a straight line as shown below:

(n^3 - n)

= n(n-1)(n+1)

since it is divisible by 3 and 2 ,because it is a multiple 3 consecutive number

if, n-1 is odd then n+1 is also odd, then it is a multiple of 9

but if, n-1 is even then n+1 is also even, then it is a multiple of 4

so, largest multiple = max(9*2, 4*3) = max(18, 12) = 18