01 Key Concepts
Function Definition
A relationship where every input (x-value) produces exactly one output (y-value).
Function Notation
f(x) is read 'f of x' and represents the output of function f for input x. f(3) means 'evaluate the function at x=3'.
The Vertical Line Test
If any vertical line crosses a graph more than once, the graph does NOT represent a function.
Domain and Range
The domain is the complete set of possible input (x) values; the range is the complete set of possible output (y) values.
Evaluating Functions
Substitute the given input value everywhere the variable appears in the function's formula, then simplify.
02 Solved Examples
Example 1 If f(x) = 2x + 3, find f(5).
- Substitute x=5: f(5) = 2(5) + 3.
- = 10 + 3.
Answer: f(5) = 13
Example 2 If g(x) = x^2 - 4, find g(-3).
- Substitute x=-3: g(-3) = (-3)^2 - 4.
- = 9 - 4.
Answer: g(-3) = 5
Example 3 Does the equation x = y^2 represent a function of x? Use the vertical line test reasoning.
- Solve for y: y = plus or minus sqrt(x).
- For a single positive x-value, there are two y-values (positive and negative square root).
- This means a vertical line at that x would cross the graph twice.
Answer: No, x=y^2 does not represent y as a function of x
03 Practice Questions
1If f(x) = 3x - 1, find f(4).
11
2If f(x) = x^2 + 2, find f(3).
11
3If f(x) = 5x, find f(0).
0
4What test determines if a graph represents a function?
The vertical line test
5If g(x) = x - 7, find g(10).
3
📄 Functions — Downloadable Worksheet
10 questions with a full answer key. Grab the PDF to print, or try the interactive version in your browser.