Integrated Math 1 / Unit 3: Functions
3.6 Representing and Comparing Functions
Notes
The same function can be written as an equation, table, graph or words. To compare functions, compare their rates of change and starting values.
- A table is linear if equal input steps give equal output steps.
- Example: inputs 0, 1, 2, 3 with outputs 5, 8, 11, 14 follow $y = 3x + 5$.
- Discrete situations (counting items) give separate points; continuous ones (time, volume) give connected graphs.
- The $y$-intercept is the starting value; the rate of change is how fast the output changes.
Practice
A table has inputs 0, 1, 2, 3 and outputs 5, 8, 11, 14. Which rule matches?
Outputs rise by 3 each step and the output at $x = 0$ is 5.
Which situation is best modeled by a discrete function?
You can only order a whole number of pizzas, so the graph is separate points.
Function $f(x) = 3x + 1$. Function $g$ has $g(0) = 2$, $g(1) = 4$ and $g(2) = 6$. Which statement is true?
$f$ changes by 3 per step and $g$ by 2. At $x = 0$, $f$ is 1 and $g$ is 2.
Ready for more? Take the Unit 3 test.