Determine which of the given functions has a greater rate of change.
Before we can determine which function has the greater rate of change, we’ll need to find the
rate of change for both, function a and function b. When working with functions, the rate of
change equals the changes in 𝑦 over the changes in 𝑥. We also write that as 𝑦 two minus 𝑦 one
equals 𝑥 two minus 𝑥 one.
Starting with function a, we’ll need to choose two points to be our 𝑥 one, 𝑦 one and our 𝑥
two, 𝑦 two. You can choose any two points on the chart. I’m going to choose one, zero and
two, two. Our first point, we label 𝑥 one, 𝑦 one. And our second point, we call 𝑥 two, 𝑦 two.
Now we plug this information into our formula. 𝑦 two equals two, 𝑦 one equals zero, 𝑥 two
equals two, 𝑥 one equals one. Two minus zero equals two. Two minus one equals one. We reduce
that to two, and the rate of change of function a equals two.
Finding the rate of change of function b is actually a little bit easier. Function b is in the
form 𝑦 equals 𝑚𝑥 plus 𝑏, which is the equation form of a straight line. And this is good news
for us. When an equation is in this form, the 𝑚 represents the rate of change. Another word that
we use here is the slope. What we do now is look at our equation, 𝑦 equals three 𝑥 plus five, and
identify which value is in the 𝑚 position. Here, the 𝑚 is three. The slope, or the rate of change,
of function b equals three.
So we have the rate of change of function b equals three. The rate of change of function a
equals two. Now we need to compare which is greater. Three is greater than two which means
the rate of change of function b is greater than the rate of change for function a.