2.1 Functions

Question 1

a rule that assigns each element in one set to a unique element in a second set

Answer 1

function

Question 2

being the only one of its kind

Answer 2

unique

Question 3

a set of ordered pairs in which no two ordered pairs have the same first coordinate and different second coordinates

Answer 3

function

Question 4

“is a function of” means

Answer 4

is determined by

Question 5

there is more than one value of the output that corresponds to the same input

Answer 5

not a function

Question 6

the input or first coordinate

Answer 6

independent variable

Question 7

the output or second coordinate

Answer 7

dependent variable

Question 8

a set of ordered pairs

Answer 8

relation

Question 9

Name the ways you can represent a relation

Answer 9

1) verbal description
2) graph
3) formula
4) equation
5) table

Question 10

How do you determine if a relation is a function if you have a list of ordered pairs?

Answer 10

check to see if any of the x’s repeat. If so, do they have the same y-coordinate? If the y-coordinates are the same for the repeated x-coordinate, then the relation is a function. If you have different y- coordinates for the same x-coordinate, then the relation is not a function.

Question 11

How do you determine if a relation is a function if you are given a graph?

Answer 11

Draw a vertical line on the graph. If the line passes the vertical line test, the relation is a function. If not, the relation is not a function.

Question 12

How do you determine if a relation is a function if you are given an equation?

Answer 12

Solve for y. Did you take an even root to solve for the value of y? If so, there would be a plus or minus in front of the root giving two outputs for the same input. Therefore, the equation is not a function. If you did not take the even root of both sides of the equation to solve for y, then it would automatically be a function for “MOST” items. There are exceptions that are not taught in this course.

Question 13

What is the vertical line test?

Answer 13

a graph is the graph of a function if and only if there is no vertical line that crosses the graph more than once.

Question 14

the set of all first coordinates of the ordered pairs

Answer 14

domain

Question 15

the set of all second coordinates of the ordered pairs

Answer 15

range

Question 16

How do you find the domain of any equation?

Answer 16

Look for places the function is undefined. Exclude these values.

Question 17

Which functions could have breaks in their domain?

Answer 17

1) functions that have variables in the denominator
2) functions with even roots
3) piece-wise defined functions (some)
4) logarithms
5) some trigonometric functions
6) circles

Question 18

How do you find the domain of a set of ordered pairs?

Answer 18

List all the x-values from least to greatest. Do not repeat values.

Question 19

How do you find the range of a set of ordered pairs?

Answer 19

List all the y-values from least to greatest. Do not repeat values.

Question 20

How do you find the domain of a function that contains an even root?

Answer 20

Set the radicand greater than or equal to zero and solve. Write the answer in interval notation.

Question 21

How do you find the domain of a function that contains a variable in the denominator?

Answer 21

Set the denominator not equal to zero and solve. Write the answer in interval notation.

Question 22

How do you find the domain of a function that contains an even root in the denominator?

Answer 22

Set the denominator > 0 and solve. Write the answer in interval notation.

Question 23

Which functions have domains of “all real numbers”?

Answer 23

All lines except vertical.
Polynomial functions
Exponential functions
Absolute value functions.
Odd root functions that are not in a denominator.
Greatest Integer functions

Question 24

provides a rule for finding the second coordinate or output

Answer 24

function notation

Question 25

the change in y-coordinates divided by the change in x-coordinates

Answer 25

average rate of change

Question 26

Formula for the difference quotient

Answer 26

Question 27

a function relating two variables in a geometric figure (formula)

Answer 27

construct