Functions
8-7Functions Defined by Equations
Overview
y = f(x) means y depends on x via the rule f. Substitute to evaluate.
Key ideas
- f(a) = output when input is a.
- Each equation y = … in terms of x defines a function (if each x gives one y).
- Treat f(x) as ‘the value of f at x.’
Worked examples
Example 1
Problem. If f(x) = 3x − 1, find f(4).
Solution. 11
Example 2
Problem. If g(x) = x^2 + 2, find g(−3).
Solution. 11
Practice
Try each one. Click Show answer when ready.
- 1.
f(x) = 2x + 5, find f(0).
- 2.
f(x) = x^2, find f(−4).
- 3.
g(x) = 10 − x, find g(7).
Challenge problems
A little tougher — great for test prep. Click Show answer when ready.
- 1.
If f(x) = 3x² − 2x + 1, find f(−2) and f(1/2).
- 2.
If g(x) = x² − 4, find all x such that g(x) = 0.