Math 103 College Algebra

42 terms

Natural numbers

counting numbers
does not include 0.

Integers

..., -3, -2, -1, 0, 1, 2, 3, ...

Rational numbers

includes 0, integers, fractions, repeating and terminating decimals

Irrational numbers

non-repeating, non-terminating decimals, ∏ (pi?), √2, √-5, ³√7

Real numbers

any number on the number line
includes rational and irrational

1.58 x 10⁵

Steps to standard equation of a circle

Take endpoints, find the center (midpoint formula), then find the radius (distance formula).

relation

a set of ordered pairs

domain

the set of x values in a relation

range

the set of y values in a relation

function

a relation in which each element in the domain corresponds to exactly one element in the range.

{ x '|' 1 ≤ x ≤ 5 }

set-builder notation
the set of all real numbers such that x is greater than or equal to 1, and less than or equal to 5.

Vertical line test

If every vertical line intersects a graph at no more than one point, then the graph represents a function.

{ x | x > -4 }

f(x) = b

f(x) = ax + b

∪

union, means "or"

means "and"

-2 < x < 2

-1 < x ≤ 3

-3 ≤ x ≤ 2

x > -3

x ≤ 1

x ≤ -2 or x > 1

(t² + 2th + h²)

Factor out the h 4th +2h² / h

= h(4t + 2h) / h (remove the h's)
= 4t + 2h

³√8

Cube root
³√8 = 2 (2 x 2 x 2 = 8)

model

A good model describes and explains current data. It should also make predictions and forecast phenomena. (2.1)

interpolation

estimating values between data points; more accurate than extrapolation. (2.1)

extrapolation

estimating values "outside" of the given data points; less accurate than interpolation. (2.1)

domain of a model

must have limits, i.e. D = 0, 1, 2, or 3. (2.1)

y-intercept

b of the function f(x) = ax + b; the point where a line intersects with the y axis. (2.1)

x-intercept

the point where a line intersects with the x axis; aka zero of f. (2.1)

slope

a of the function (f(x) = ax + b; indicates the number of units on the y axis a line rises or falls for every one unit on the x axis. (1.4)

Modeling with a Linear Function

f(x) = (constant rate of change)x + (initial amount)

approximate linear data

1. find the slope (a) between data sets using slope formula. 2. determine the y-intercept (b). 3. use f(x) = ax + b function.

constant function

A function f represented by f(x) = b, where b is a constant (fixed number), is a constant function. (1.4)

linear function

a function f represented by f(x) = ax + b, where a and b are constants, is a linear function.

slope

5

the slope is aka

average rate of change