The notation, ƒ(x), introduces a function. Use this article to answer the following questions.
- What are some examples of ƒ(x)?
- What do these examples mean?
- How is ƒ(x) used in the real world?
- What are the steps to finding a specific value of a function?
Examples of ƒ(x) Decoded
- ƒ(x) = x + 3 (The value of x determines ƒ(x).)
- ƒ(t) = 3t3 (The value of t determines ƒ(t).)
- ƒ(s) = -100s2 + 5s (The value of s determines ƒ(s).)
Real World Examples of ƒ(x)
The real world — round, fast-paced, expensive — relies on functions.
- The circumference of a circle, C(r), depends on its radius, r. C(r) = 2Πr
- The area of a circle, A(r), depends on its radius, r. A(r) = Πr2
- The distance, D(r), from home to work depends on the time, t, spent driving at an average speed of 50 miles an hour. D(r) = 50t
- The value, V(t), of a $500 investment, with an annual return of 4%, depends on t years. V(t) = 500(1.04)t
Finding Specific Values of Functions
Use these examples to learn how to evaluate a function, or to find the specific value of ƒ(x) at a certain point.
ƒ(x) = x + 3; Find ƒ(3)
- ƒ(3) = 3 + 3 (Replace x with 3.)
- ƒ(3) = 6 (Simplify.)
g(x) = 2x3 + 5; Find g(-4)
- g(-4) = 2(-4)3 + 5 (Replace x with -4)
- g(-4) = 2 * -64 + 5 (Simplify.)
- g(-4) = -128 + 5 (Simplify.)
- g(-4) = -123 (Simplify.)
h(x) = sinx; Find h(180°)
- h(180°) = sin180° (Replace x with 180°.)
- h(180°) = 0 (Use the calculator to simplify.)
1. ƒ(x) = 7x - 3; Find ƒ(0).
2. ƒ(t) = |5t|; Find ƒ(2).
3. g(x) = x2 + 8x - 6; Find g(1).
4. ƒ(b) = 3b; Find ƒ(3).
5. ƒ(x) = sinx; Find ƒ(45°).
6. ƒ(x) = cosx; Find ƒ(90°).
7. ƒ(c) = .25c ; Find ƒ(-2).
8. ƒ(x) = -10x + 5; Find ƒ(-10).
9. ƒ(r) = 2Πr2 + 2Πr; Find ƒ(4).
10. ƒ(t) = 100(1.10)t; Find ƒ(4).