Evaluating Functions, Function vocabulary, Functions (Algebra)

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Vertical Line Test

A test use to determine if a relation is a function. A relation is a function if there are no vertical lines that intersect the graph at more than one point.

dependent variable

A variable (y) that depends on one or more other variables

domain

All the values that go into a function

f(-2) = 7, f(3) = 9

(4, -2), (1, 8), (-3, 5), (-2, 7), (1, 9), (3, 9) Evaluate f(-2). Evaluate f(3).

Function f(x)

A relation for which each element of the domain corresponds to exactly one element of the range

f(-2) = -23, f(3) = 7

f(x) = 4x - 3 + 2x - 8 Evaluate f(-2). Evaluate f(3)

f(-2) = -14, f(3) = 1

f(x) = 3x - 8 Evaluate f(-2). Evaluate f(3)

f(-2) = -2, f(3) = -1

Evaluate f(-2). Evaluate f(3).

f(-2) = 0, f(3) = -1

Evaluate f(-2). Evaluate f(3).

f(-2) = 1, f(3) = -3

Evaluate f(-2). Evaluate f(3).

f(-2) = 2, f(3) = 10

Evaluate f(-2). Evaluate f(3).

f(-2) = 4, f(3) = 9

Evaluate f(-2). Evaluate f(3).

x-coordinate

The horizontal value in a pair of coordinates

Range

The set of outputs or y-values

Independent variable

The variable that represents the input and causes the change in the dependent variable; x-axis label

y-coordinate

The vertical value in a pair of coordinates

f(-2) = -2, f(3) = 18

This is a linear function. Evaluate f(-2). Evaluate f(3).

nonlinear function

a function that does not have a constant rate of change

linear function

any function that has a constant rate of change; the function has either one or two variables with no exponents or powers

run

change in the x-values

rate of change

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

rise

change in the y-values

relation

collection of ordered pairs containing one object from each set.

f(-2) = -9 f(3) = 1

f(x) = -(2x - 3) + 4(x - 2) Evaluate f(-2). Evaluate f(3).

f(-2) = 6, f(3) = -19

f(x) = -2(x - 1) - 3(x + 2) Evaluate f(-2). Evaluate f(3).

f(-2) = 17, f(3) = -3

f(x) = -3(2x - 5) + 2(x - 3) Evaluate f(-2). Evaluate f(3)

qualitative graph

graphs that are used to represent situations that do not necessarily have numerical values

slope

how steep a straight line is

unit rate

ratio of two measurements in which the second term is 1

mapping diagram

shows how each element of an input is paired with each element of an output.

input

the known variable.

coordinate plane

the plane containing the "x" axis and "y" axis.

output

the unknown variable.

y-intercept

the value where a line crosses the y-axis of a graph

x-intercept

the value where a line intersects the x-axis of a graph

ordered pair

two numbers written in a certain order; usually written in parentheses like this: (4,5)


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