Linear functions

Question 1

arithmetic sequence

Answer 1

a linear function with a domain of positive consecutive integers in which the difference between any two consecutive range terms is equal

Question 2

asymptote

Answer 2

a line that an exponential graph gets closer and closer to, but never crosses or touches

Question 3

common difference

Answer 3

the number added to each consecutive term in an arithmetic sequence

Question 4

continuous

Answer 4

having no breaks

Question 5

curve

Answer 5

the graphical representation of the solution set for y = f(x); in the special case of a linear equation, it will be a line

Question 6

dependent variable

Answer 6

the output variable of a function

Question 7

discrete

Answer 7

individually separate and distinct

Question 8

domain

Answer 8

the set of all inputs of a function; the set of x-values that are valid for the function

Question 9

end behavior

Answer 9

the behavior of the graph as x becomes larger or smaller

Question 10

equation

Answer 10

a mathematical sentence that uses an equal sign (=) to show that two quantities are equal

Question 11

explicit equation

Answer 11

an equation used to find the nth term of a sequence; some examples are a_n = a₁ + (n – 1)d and a_n = a₁ • r _{n – 1}

Question 12

exponential function

Answer 12

a function that has a variable in the exponent; the general form is f(x) = ab^x, where a is the initial value, b is the rate of decay or growth, x is the time, and f(x) is the final output value

Question 13

expression

Answer 13

a combination of variables, quantities, and mathematical operations; 4, 8x, and b + 102 are all examples.

Question 14

extrema

Answer 14

the minima and maxima of a function

Question 15

factor

Answer 15

one of two or more numbers or expressions that when multiplied produce a given product

Question 16

function

Answer 16

a relation in which every element of the domain is paired with exactly one element of the range; that is, for every value of x, there is exactly one value of y.

Question 17

function notation

Answer 17

a way to name a function using f(x) instead of y

Question 18

geometric sequence

Answer 18

an exponential function that results in a sequence of numbers separated by a constant ratio

Question 19

growth factor

Answer 19

the number multiplied by each consecutive term in a geometric sequence, also known as the constant ratio

Question 20

growth rate

Answer 20

the growth factor minus 1

Question 21

independent variable

Answer 21

the input variable of a function

Question 22

integer

Answer 22

a number that is not a fraction or a decimal

Question 23

irrational numbers

Answer 23

numbers that cannot be written as a/b, where a and b are integers and b ≠ 0; any number that cannot be written as a decimal that ends or repeats

Question 24

linear equation

Answer 24

an equation that can be written in the form ax + by = c, where a, b, and c are rational numbers; can also be written as y = mx + b.

Question 25

linear function

Answer 25

a function that can be written in the form f(x)=mx + b, in which m is the slope, b is the y-intercept, and the graph is a line

Question 26

natural numbers

Answer 26

the set of positive integers {1, 2, 3, …, n}

Question 27

ordered pair

Answer 27

a pair of values (x, y) where the order is significant

Question 28

range

Answer 28

the set of all outputs of a function; the set of y-values that are valid for the function

Question 29

rate of change

Answer 29

a ratio that describes how much one quantity changes with respect to the change in another quantity; also known as the slope of a line

Question 30

rational numbers

Answer 30

a number that can be written as a/b , where a and b are integers and b ≠ 0; any number that can be written as a decimal that ends or repeats

Question 31

real number

Answer 31

the set of all rational and irrational numbers

Question 32

recursive equation

Answer 32

an equation used to find the next term of a sequence when the previous term or terms are known; some examples are a_n = a_{n – 1} + d and a_n = a_{n – 1} • r

Question 33

relation

Answer 33

an ordered relationship between two sets of elements

Question 34

relative maximum

Answer 34

the greatest value of a function for a particular interval of the function

Question 35

relative minimum

Answer 35

the least value of a function for a particular interval of the function

Question 36

system of equations

Answer 36

a set of more than one equation

Question 37

transformation

Answer 37

moving a graph, including reflections, rotations, and translations

Question 38

translation

Answer 38

moving a graph either vertically, horizontally, or both, without changing its shape; a slide

Question 39

undefined slope

Answer 39

the slope of a vertical line

Question 40

variable

Answer 40

a letter used to represent a value or unknown quantity that can change or vary in an expression or equation

Question 41

vertical shift

Answer 41

number of units the graph of the function is moved up or down; a translation

Question 42

whole numbers

Answer 42

the set of natural numbers that also includes 0; {0, 1, 2, 3, …}

Question 43

x-intercept

Answer 43

the point at which the line intersects the x-axis at (x, 0)

Question 44

y-intercept

Answer 44

the point at which a line or curve intersects the y-axis at (0, y)

Question 45

zero slope

Answer 45

the slope of a horizontal line

Question 46

decreasing interval

Answer 46

a portion of a function where the y-values are decreasing over the interval

Question 47

increasing interval

Answer 47

a portion of a function where the y-values are increasing over the interval

Question 48

positive interval

Answer 48

a portion of a function where the y-values are greater than 0 for all x-values

Question 49

negative interval

Answer 49

a portion of a function where the y-values are less than 0 for all x-values

Question 50

solution set

Answer 50

the set of ordered pairs that represent all of the solutions to an equation or a system of equations