Comparing Linear and Exponential Functions
F.LE.1 Distinguish between situations that can be modeled with linear...and...exponential functions. Also F.IF.6, F.LE.1.a, F.LE.3
Objective:
The student's will be able to compare the properties of linear and exponential functions.
We can identify a similarity between linear and exponential functions by plugging in an x value into the function to get a y value output. As we can see, using a linear or exponential function creates a y value output. We can take any x value to plug it into the function to get the y value.
For example: we can take a linear function of y=2x+1.
Now, let's go ahead and plug in some values for x.
x=0; y=2(0)+1=0+1=1 y=1
x=1; y=2(1)+1=2+1=3 y=3
x=2; y=2(2)+1=4+1=5 y=5
x=3; y=2(3)+1=6+1=7 y=7
Now let's see an example of an exponential function of
Average rate of change:
The average rate of change is having an f(x) over an interval of a and b where a is less than or equal to x is less than or equal to b.
Let's look at a example to see how we can use this to solve the rate of change. In this example, we can see that we are given a function g(x) over a certain interval.
Step 1: take each number from the interval which would be 1 and 6
Step 2: plug in those numbers into the function to produce a value. In this case, it is -8 and 162.
Step 3: take the average rate of change formula and plug in those numbers to get an answer of 34.
Olmos 5.3 comparing linear and exponential functions week 6 day 1.pdf