Lesson 2: Evaluating Functions

To evaluate a function,

1.Substitute the value in function of x.

2.Replace the all the variables with the number or expression for the func- tion’s variable.

3.Evaluate and simplify the function.

Example 1: Given the function: f(x ) = 2 x+ 1, nd f(6).

Substitute 6 in place holder x,

f(6) = 2 x+ 1

Replace the all the variables with 6,

f(6) = 2(6) + 1

Then evaluate and simplify the function. f(6) = 12 + 1

f (6) = 13

Therefore, f(6) = 13. It can also write in ordered pair which is (6,13).

Example 2:

Given the function f(x ) = x2

+ 2 x+ 4 when x= 4.

Substitute -4 in the place holder x,

f ( 4) = x2

+ 2 x+ 4

Replace the all the variables with 6, f( 4) = ( 4) 2

+ 2( 4) + 4

Then evaluate and simplify the function. f( 4) = (16) + ( 8) + 4

f ( 4) = 12

Therefore, f( 4) = 12 or simply as ( 4;12) :

Example 3:

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Given

g(x ) = x2

+ 2 x- 1. Find g(2y).

Answer in terms of y.

g(2 y) = x2

+ 2 x 1

g (2 y) = (2 y)2

+ 2(2 y) 1

g (2 y) = 4 y2

+ 4 y 1

Therefore, 4( y)2

+ 4 y 1:

Example 4:

Given f(x ) = 2 x2

+ 4 x- 12, nd f(2 x+ 4).

Solution: f(2 x+ 4) = 2 x2

+ 4 x 12

= 2(2 x+ 4) 2

+ 4(2 x+ 4) 12

= 2(2 x+ 4)(2 x+ 4) + 4(2 x+ 4) 12

= 2(4 x2

+ 16 x+ 16) + 4(2 x+ 4) 12

= (8 x2

+ 32 x+ 32) + (8 x+ 16) 12

Combine like terms f(2 x+ 4) = 8 x2

+ (32 x+ 8 x) + (32 + 16 12)

= 8 x2

+ 40 x+ 36

= 2(2 x2

+ 10 x+ 9)

Therefore, f(2 x+ 4) = 2(2 x2

+ 10 x+ 9).

Example 5:

Given f(x ) = x2

-x – 4. If f(a ) = 8, what is the value of a?

Solution: Equate the function by x2

-x 4 = 8

x 2

x 4 = 8

x 2

x 12 = 0

( x 4)( x+ 3) = 0

x 4 + 0; x+ 3 = 0

x = 4; x= 3

Therefore, the value of a can be either 4 or -3.

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Exercises:

Evaluate each function

Given the functions:

1. k(x ) = x + 2, nd k(-5)

2. p(x ) = 2 x, nd p(-4)

3. g(n ) = n2

+ 3, nd g(8)

4. g(x ) = x3

+ 5 x, nd g(5)

5. h(n ) = n3

+ 3 n2

, nd h(-5)

6. w(a ) = a2

+ 5 a, nd w(7)

7. p(a ) = a3

– 4 a, nd p(-6)

8. h(n ) = 4 3

n

+ 8 5

, nd

h(-1)

9. f(x) = -1 + 1 4

x;

nd f3 4

10. h(n) = n3

+ 6 n, nd h(4)

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Answers to Evaluating Functions Exercises:

1. 11

2. -18

3. 67

4. 150

5. -50

6. -14

7. -192

8. 4 15

9. – 13 16

10. 88

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