Evaluate a Function Tutorial and Worksheet

The notation, ƒ(x), introduces a function. Use this article to answer the following questions.
(Answers here)

• 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.

»»»Example 1

ƒ(x) = x + 3; Find ƒ(3)

1. ƒ(3) = 3 + 3 (Replace x with 3.)
2. ƒ(3) = 6       (Simplify.)

»»»Example 2

g(x) = 2x³ + 5; Find g(-4)

1. g(-4) = 2(-4)³ + 5       (Replace x with -4)
2. g(-4) = 2 * -64 + 5     (Simplify.)
3. g(-4) = -128 + 5         (Simplify.)
4. g(-4) = -123               (Simplify.)

»»»Example 3

h(x) = sinx; Find h(180°)

1. h(180°) = sin180°   (Replace x with 180°.)
2. h(180°) = 0             (Use the calculator to simplify.)

Exercises

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) = 3^b; Find ƒ(3). 

 

 

5. ƒ(x) = sinx; Find ƒ(45°). 

 

 

6. ƒ(x) = cosx; Find ƒ(90°). 

 

 

7. ƒ(c) = .25^c ; 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). 

 

 

See Answers