1. 7.3 Power Functions and Function Operations
Goals
Perform operations with functions, including power functions.
Use power functions and function operations to solver real-life problems.

2. Evaluate each function for when x = -2
f(x) = 2x + 5
f(x) = 2(-2) + 5
f(x) =
f(x) = 1
g(x) = x2 – 1
g(x) = (-2)2 – 1
g(x) = 4 -1
g(x) = 3

3. Domain The numbers that CAN be plugged in for x in a function
Have to look at beginning function through the ending function for domain!!!
Try to find the values that CANNOT be plugged in to determine domain
1. Can’t divide by zero (undefined)
2. Can’t take even root of a negative number
If there are no restrictions on x, then the domain is “all reals”

4. Operations with Functions
The four basic operations can be applied to any function.
Let’s perform the basic operations with this example: f(x) = 2x + 5 g(x) = x2 - 1

5. Addition of Functions EX: f(x) = 2x + 5 g(x) = x2 - 1
f(x) + g(x) = (2x + 5) + (x2 - 1)
= 2x x2 - 1
= x2 + 2x + 4
Domain = “all reals”
Is f(x) + g(x) = g(x) + f(x)?

6. Subtraction of Functions
EX: f(x) = 2x + 5 g(x) = x2 - 1
f(x) – g(x) = (2x + 5) – (x2 - 1)
= 2x + 5 – x2 + 1
= -x2 + 2x + 6
Domain = “all reals”
Is f(x) – g(x) = g(x) – f(x)?

7. Multiplication of Functions
EX: f(x) = 2x + 5 g(x) = x2 - 1
f(x) · g(x) = (2x + 5)(x2 - 1)
= 2x3 - 2x + 5x2 - 5
= 2x3 +5x2 - 2x - 5
Domain = “all reals”
Is f(x) · g(x) = g(x) · f(x)? ·

8. Division of Functions EX: f(x) = 2x + 5 g(x) = x2 - 1
f(x) / g(x) = (2x + 5) / (x2 - 1)
Domain =
Is f(x) / g(x) = g(x) / f(x)? ·

9. Composition Plug one function into another
Put one function in place of x

10. Composition of Functions: Example 1
f(x) = 2x + 3 and g(x) = x2 + 5
Find: f(g(x))
f(x2 + 5) = 2(x2 + 5) + 3
= 2x
= 2x2 + 13
Domain = “all reals”

11. Composition of Functions: Example 2
f(x) = 2x + 3 and g(x) = x2 + 5
Find: g(f(x))
g(2x + 3) = (2x + 3)2 + 5
= (2x + 3)(2x + 3) + 5
= 4x2 + 6x + 6x
= 4x2 + 12x +14
Domain = “all reals”

12. Composition of Functions: Example 3
f(x) = 2x + 3 and g(x) = x2 + 5
Find: f(f(x))
f(2x + 3) = 2(2x + 3) + 3
= 4x
= 4x + 9
Domain = “all reals”

13. One More Example f(x) = 3x and g(x) = x1/4 f(x) / g(x)
Domain = “positive real #s” ·

14. Review and some more!
Domain: look at beginning through ending
Can’t divide by zero
Can’t take even root of a negative number
Difference between “nonnegative” and “positive” real numbers
Nonnegative Real Numbers
Includes “0”
Positive Real Numbers
Does NOT include “0”

15. EX: f(x) = 2x + 5 g(x) = x2 - 1
f(x) + g(x) = (2x + 5) + (x2 - 1)
= 2x x2 - 1
= x2 + 2x + 4
Domain = “all reals”
EVALUATE for x = -4
= (-4)2 + 2(-4) + 4 =
= 12

16. Homework P.418 #28-31 all (answer questions & evaluate each for x=3)

17. 7.3 Power Functions and Function Operations
Day 2

18. Go over:

19. Interval Notation Brackets mean > or < [ ]
Parenthesis mean > or < ( )
Interval Notation

20. Domain for 3 more…..
Positive v. Nonnegative

21. Homework 7.3 WS Practice B #2 - 16 even
# all (answer question & evaluate each problem for x=2)
Write out domain for ALL in “Interval Notation”