Algebra 1 - Unit 3 Review

Front 1

Relation

Back 1

Pairs inputs with outputs

Front 2

Function

Back 2

A relation that pairs each input with exactly one output.

Front 3

Vertical Line Test

Back 3

A graph represents a function when no vertical line passes through more than one point on the graph.

Front 4

Domain

Back 4

The set of all the possible input (x) values

Front 5

Range

Back 5

The set of all the possible output (y) values

Front 6

Independent Variable

Back 6

an input value, x-value

Front 7

Dependent Variable

Back 7

an output value, y-value

Front 8

Linear Function

Back 8

a function whose graph is a nonvertical line

Front 9

Nonlinear Function

Back 9

a function that does not have a constant rate of change

Front 10

Discrete domain

Back 10

a set of input values that consists of only certain numbers in an interval

Front 11

Continuous domain

Back 11

a set of input values that consists of all numbers in an interval

Front 12

Function Notation

Back 12

When f(x) (said "f of x") is used in place of y

Front 13

Horizontal Lines are of the form

Back 13

y = b, where b is a constant

Front 14

Vertical Lines are of the form

Back 14

x = b, where b is a constant

Front 15

Standard Form of a Linear Equation is:

Back 15

Ax + By = C, x = C/A is the x-intercept and y= C/B is the y-intercept

Front 16

x - intercept

Back 16

the x-coordinate of a point where the graph crosses the x-axis

Front 17

y - intercept

Back 17

the y-coordinate of a point where the graph crosses the y-axis

Front 18

Slope

Back 18

Front 19

Slope Intercept Form

Back 19

y = mx + b,

m is the slope b is the y-intercept

Front 20

Constant Function

Back 20

a linear function written in the form y=b since the slope would be 0. This is seen as a horizontal line.

Front 21

Parent Function

Back 21

The most basic function in a family of functions.

Front 22

Transformation

Back 22

Changes the size, shape, position, or orientation of a graph.

Front 23

Translation

Back 23

A transformation that shifts the graph horizontally or vertically

Front 24

Parent Function of a Linear Function

Back 24

f(x) = x

Front 25

Horizontal Translation

Back 25

g(x) = f(x-h)

When h is positive, (looks like subtraction) it is a horizontal translation to the right.

When h is negative, (looks like addition) it is a horizontal translation to the left.

Front 26

Horizontal Translation of f(x) = x 3 units to the left

Back 26

g(x) = f(x + 3)

Front 27

Vertical Translation

Back 27

g(x) = f(x) + k

When k is positive, it is a vertical translation up.

When k is negative, it is a vertical translation down.

Front 28

Vertical translation of f(x) = x, 7 units down

Back 28

g(x) = f(x) -7

Front 29

Reflection over the x-axis of f(x) = x

Back 29

g(x) = -f(x)

Front 30

Reflection over the y-axis of f(x) = x

Back 30

g(x) = f(-x)

Front 31

Vertical Shrink

Back 31

g(x) = af(x) when 0 < a < 1

Front 32

Vertical Stretch

Back 32

g(x) = af(x) when a > 1

Front 33

The graph of an absolute value function is always shaped like what letter?

Back 33

V

Front 34

Vertex Form of an Absolute Value Function

Back 34

g(x) = a|x-h| + k

The vertex would be (h,k)

Front 35

What is the vertex of g(x) = 3|x+7|-4?

Back 35

(-7, -4)

Front 36

Parent Function of an Absolute Value Function

Back 36

f(x) = |x|

Front 37

f(x) = |x| ; g(x) = |x-1|+2

Describe the transformation from f to g

Back 37

The graph of g is a horizontal translation 1 unit right and a vertical translation 2 units up of the graph of f.

Front 38

f(x) = x ; g(x) = 5f(x)

Describe the transformation from f to g

Back 38

The graph of g is a vertical stretch by a factor of 5 of the graph of f.