Question

Which of the following represents a function with the greatest rate of change?

Answer 1

It is C because when you calculate you can see I it has more change

Answer 2

So the rate of change can be found in different places.

For the first one:

This equation is in slope-intercept form, or y = mx + b.

m would be the slope/rate of change, and b the y intercept. (x and y would just be any sets of ordered pairs that fit into the equation.)

So if you look at which number is in the m spot, or the rate of change spot, you see that 5 is the rate of change.

For the second one: The formula for slope is:

m = $\frac{ y_{2} - y_{1} }{x_{2} - x_{1} }$

So just put in any ordered pairs in. I'm just going to put in the ordered pairs, (6, 30) and (4, 22).

Or,

m = (30 - 22) / (6 - 4)

Or,

m = 8/2

Or 4.

For the third one:

You can use the same formula as I stated above.

So you have to look for two ordered pairs here, two points.

So you can estimate that two of the points are: (0, 3) and (-2, -9).

So then just solve for that.

(-9 - 3) / (-2 - 0) = -12 / -2 = 6

For the last one:

Again, use the same equation.

m = (7 - 1) / (-1 - (-3))

 m = 6/2 

m = 3

So the one with the greatest rate of change would be C.