Unit 6, Lesson 20
Changes over Equal Intervals
Algebra 1
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Here is a graph of
Graph of an increasing linear function, x y plane, origin O. Horizontal axis, scale 0 to 10, by 5’s. Vertical axis, scale 0 to 15, by 20’s. The function starts at (0 comma 3) and goes through (1 comma 7) , ( 2 comma 9), (3 comma 11), (4 comma 13) and (5 comma 15).
Here is an expression we can use to find the difference in the values of
Does this expression have the same value as what you found in the previous questions? Show your reasoning.
Linear and exponential functions each behave in a particular way every time their input value increases by the same amount.
Take the linear function
Graph of an increasing linear function, x y plane, origin O. Horizontal axis, scale 0 to 10, by 5’s. Vertical axis, scale 0 to 60, by 20’s. The function starts at (0 comma 3) and goes through (7 comma 38) and (8 comma 43). A horizontal green dashed line over green 1 goes from (7 comma 38) for 1 unt, then up to (8 comma 43) with a green 5 next to it for 5 units.
The value of
This tells us that whenever
Now let's look at an exponential function
Graph of an increasing exponential function, x y plane, origin O. Horizontal axis, scale 0 to 10, by 5’s. Vertical axis, scale 0 to 60, by 20’s. The function starts at the vertical axis and goes through (3 comma 8), (4 comma 16) and (5 comma 32).
The value of
This means that whenever
A linear function always increases (or decreases) by the same amount over equal intervals. An exponential function increases (or decreases) by equal factors over equal intervals.