Functions
Definitions, Properties & Formulas
Relation / a set of ordered pairs (x, y)Domain / the set of all x-values of the ordered pairs
Range / the set of all y-values of the ordered pairs
Function / a relation in which each element of the domain is paired with exactly one element in the range.
Vertical Line Test (VLT) / If any vertical line passes through two or more points on the graph of a relation, then it does not define a function.
Horizontal Line Test (HLT) / If any horizontal line passes through two or more points on the graph of a relation, then its inverse does not define a function.
One-to-One Functions / a function where each range element has a unique domain element
(use HLT to determine)
Onto Functions / All values of y are accounted for
Inverse Relations & Functions / f -1(x) is the inverse of f(x), but f -1(x) may not be a function
(use HLT to determine)
Writing Inverse Functions / To find f -1(x):
(1) let f(x) = y
(2) switch the x and y variables
(3) solve for y
(4) let y = f -1(x)
Operations with Functions / sum: (f + g)(x) = f(x) + g(x)
difference: (f – g)(x) = f(x) – g(x)
product: (f · g)(x) = f(x) · g(x)
quotient:
College Algebra: Functions and Models Name:______
Review- Function test
Date:______
Objective: To review the material that you will be tested on as part of Test #1-Functions. These topics are in the outline below:
Functions
a. Identifying functions
b. Domain and Range of functions
c. Evaluating functions graphically
d. Evaluating functions algebraically
e. Identifying one-to-one functions
f. Identifying onto functions
g. Composition of functions
h. Inverse functions
i. Operations with Functions
Below you will find a sample of the types of problems you can expect to see on the test.
a. Which graph of a relation is also a function?
(a) (b) (c) (d)
b. Determine the Domain and Range of:
i. ii.
c. If the following graph is y = f(x), what is the value of f(1)?
(a) -1 (b) -2 (c) 1 (d) 2
d. Given f(x) = 4x – 7 and g(x) = 2x – x2, evaluate f(2) + g(-1)
e. Which function is not one to one?
(a) (b) (c) (d)
f. Which function is not onto?
(a) (b) (c) (d)
g. Given , find .
h. Find the inverse of the following and state the domain.
- f(x) = 5x + 2 b.
i. Perform the four basic operations on and determine the domain of the result.
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