Integrated Math 1 / Unit 3: Functions
3.2 Function Notation
Notes
In function notation, $f(x)$ means "the output of function $f$ when the input is $x$." It does not mean $f$ times $x$.
- To evaluate, substitute the input into the rule: if $f(x) = 3x - 5$, then $f(4) = 3(4) - 5 = 7$.
- Use parentheses when substituting negatives: $g(x) = x^2 + 2x$, so $g(-3) = (-3)^2 + 2(-3) = 3$.
- $f(a) = b$ means the point $(a, b)$ is on the graph.
- In context, $f(2) = 10$ tells you the output for the input 2, with units.
Practice
If $f(x) = 3x - 5$, what is $f(4)$?
$3(4) - 5 = 12 - 5 = 7$.
If $g(x) = x^2 + 2x$, what is $g(-3)$?
$(-3)^2 = 9$ and $2(-3) = -6$, so $9 - 6 = 3$.
The function $h(t)$ gives a plant's height in cm after $t$ weeks. What does $h(2) = 10$ mean?
The input is time (2 weeks) and the output is height (10 cm).
Ready for more? Take the Unit 3 test.