Download Name:____________________________________________________ Date:__________ Period:_______ More Functions Review!!!

Name:____________________________________________________
More Functions Review!!!
Date:__________ Period:_______
Algebra 2
More Functions Review
I. Inverse Functions: To find the inverse of a function, we must switch the x and y
values. When solving this in a form of an equation:
(1) rewrite all function notation in the form y =
(2) switch x and y
(3) solve for y
(4) rewrite in inverse notation
Find the inverse of the following functions.
1.)
2.)
3.)
4.)
5.)
6.)
II. Domain: The domain of a function is all of the x-values. Steps to finding a domain.
There are times when the domain is restricted.
(1) If there is a fraction – set the denominator
, then solve.
(2) If there is a radical – set the number inside the radical > 0, then solve.
(3) If a radical is in the denominator – set the number inside the radical to be
> 0, then solve.
(4) ALL OTHER TIMES THE DOMAIN IS ALL REAL NUMBERS
Find the domain of the following functions.
1.)
2.)
3.)
4.)
5.)
6.)
III. Composite Functions: A composite function is a function within a function. For
these problems, you need to start with the inner most function and then work your
way from the inside out. Whatever term is inside the parenthesis needs to replace
the x.
To answer the following composite functions, use the given functions:
1.)
2.)
3.)
4.)
5.)
6.)
Review Topics
IV. Complex Fractions: A complex fraction is a fraction within a fraction.
To reduce a complex fraction, you must:
(1) Find an LCD of all of the “little” fractions (factor all denominators first).
(2) Multiply each “little” fraction by the LCD.
(3) Factor both the numerator and denominator.
(4) Reduce
Simplify each complex fraction.
1.)
2.)
3.)
4.)
5.)
6.)
V. Rational Expressions: These are fractions.
When Multiplying Rational Expressions:
(1) Factor every denominator & numerator.
(2) Reduce any numerator with any denominator.
(3) Multiply across the numerator and across the denominator.
(4) Leave final answer in factored form.
When Dividing Rational Expressions:
(1) Keep, Change, Flip.
(2) Follow the same steps as in multiplication.
Express all answer in simplest form.
1.)
2.)
3.)
4.)
5.)
6.)
Answer Key:
I. Inverse Functions
1.)
2.)
3.)
4.)
5.)
6.)
1.)
2.)
3.)
4.)
5.)
6.)
1.) 188
2.)
3.)
4.)
5.)
6.)
1.)
2.)
3.)
4.)
5.)
6.)
1.)
2.)
3.)
4.)
5.)
6.)
II. Domain
III. Composite Functions
IV. Complex Fractions
V. Rational Expressions