Download 11/15 Power Functions guided notes File

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Sequential Trigonometry
Power Functions
Guided Notes
Do now: Match the function with the type.
1. f(x) = 3x2
A. constant
2. f(x) = -6
B. linear
3
3. f(x) = -4x
C. quadratic
4. f(x) = 5x
D. cubic
All of these are examples of ____________________ functions.
Coefficients must be ________________________
Exponents must be __________________________
Power function: has the form f(x) = axb
Coefficient (____) must be ________________
Exponent (____) must be ___________________
If b is a positive integer, then the power function is a _________________.
Example: f(x) = 2x1/3 is a power function. It looks like this:
We can add, subtract, multiply, or divide two power functions to get a new function, h(x).
Remember that like terms have the same ___________ raised to the same ___________.
You cannot use the rules of exponents on a sum or difference (they’re only for products and
quotients).
Operation
Example 0: f(x) = 3x, g(x) = x1/4
Addition
h(x) = f(x) + g(x) = 3x + x1/4
(Note: No like terms to combine)
Subtraction
h(x) = f(x) – g(x) = 3x – x1/4
(Note: No like terms to combine)
h(x) = f(x)g(x) = (3x)(x1/4) = 3x1+1/4
Multiplication
= 3x4/4 + 1/4 = 3x5/4
Division
h(x) 
f (x) 3x

 3x11/ 4
g(x) x1/ 4
 3x 4 / 4 1/ 4  3x 3 / 4

Example 1: f(x) = 3x -1, g(x) = -6x1/2
Domain of Power Functions:
If the root is even, the domain excludes _____________ x-values.
If there is a quotient, the domain excludes x-values that make the denominator ______— even if the
denominator goes away when you simplify.
Otherwise, the domain of a power function is ______________________.
Example 2: State the domain of each of the following.
d) 3x2/3 – 4:
a) 3x1/5 + x1/4:
b) 3x5/4:
e)
5x
:
x 2
c) 3x3 – 7x2 + 1:

f) 5x2 + 10x:
Example 3: Let f(x) = -2x2/3 and g(x) = 7x2/3. Find the following.
a) f(x) + g(x)
b) f(x) – g(x)
c) the domains of parts a) and b).
Example 4: Let f(x) = 3x and g(x) = x1/5. Find the following.
a) f(x)g(x)
b)

f (x)
g(x)
c) the domains of parts a) and b).
h(x) = 3x4/5
h(x) = 3x/x1/5