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Flashcards in Linear functions Deck (50)
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1

arithmetic sequence

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

2

asymptote

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

3

common difference

the number added to each consecutive term in an arithmetic sequence

4

continuous

having no breaks

5

curve

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

6

dependent variable

the output variable of a function

7

discrete

individually separate and distinct

8

domain

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

9

end behavior

the behavior of the graph as x becomes larger or smaller

10

equation

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

11

explicit equation

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

12

exponential function

a function that has a variable in the exponent; the general form is f(x) = abx, 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

13

expression

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

14

extrema

the minima and maxima of a function

15

factor

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

16

function

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.

17

function notation

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

18

geometric sequence

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

19

growth factor

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

20

growth rate

the growth factor minus 1

21

independent variable

the input variable of a function

22

integer

a number that is not a fraction or a decimal

23

irrational numbers

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

24

linear equation

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.

25

linear function

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

26

natural numbers

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

27

ordered pair

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

28

range

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

29

rate of change

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

30

rational numbers

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