Integrated Math 2 / Unit 5: Modeling with Functions
5.1 Linear, Quadratic and Exponential Patterns
Notes
Tables of equally spaced $x$-values reveal the type of function.
- Linear: constant first differences (add the same amount each step).
- Quadratic: constant second differences (the differences change by the same amount).
- Exponential: constant ratio (multiply by the same factor each step).
- Example: $2, 5, 10, 17$ has first differences $3, 5, 7$ and second differences $2, 2$, so it is quadratic.
Practice
The outputs of a function for $x = 0, 1, 2, 3$ are $1, 3, 9, 27$. What type is it?
Each output is 3 times the previous one, a constant ratio.
The outputs for $x = 0, 1, 2, 3$ are $2, 5, 10, 17$. What type is it?
First differences are 3, 5, 7. Second differences are constantly 2.
The outputs for $x = 0, 1, 2, 3$ are $5, 9, 13, 17$. What type is it?
The first differences are always 4.
Ready for more? Take the Unit 5 test.