Function

A relation that assigns exactly one value in the range to each value of the domain.

Pictures/Examples

Function

Not a Function

1

1

2

2

One-to-one mapping

A variable that provides the input values of a function.

Independent quantity

Pictures/Examples This side of the table

x 1 2 3

y 3 6 9

Usually “Time” is.. y

The x-axis x This side of the graph

Dependent quantity

Pictures/Examples This side of the table

x 1 2 3

y 3 6 9

A variable that provides the output values of a function.

Usually “Distance” is.. y

This side of the graph

The y-axis x

Domain Pictures/Examples

The possible values for the input, or the independent variable, of a function.

This side of the table

x f(x) -5 18 0 22 10.5 32.5

From -4 to 3

(4  x  3)

Range

Pictures/Examples

The possible values for the output, or dependent variable, of a function.

This side of the table

x

y

-5 0 7

25 0 49

From 0 to 4

(0  y  4)

Continuous

Data where numbers between any two data values have meaning.

Pictures/Examples

Temperature, length, or weight Yes

No

Discrete

Data that involve a count of items.

Pictures/Examples

Number of people or number of cars

No

Yes

Intercepts (x- and y-) Pictures/Examples

The x- or ycoordinate of the point where a line crosses the x- or yaxis. Where the graph hits the x- or the y- axis.

This is the y- one (3, 0) is an x- one

This is the x- one

(0, 3) is a y- one

Linear Pictures/Examples

Yes

An equation or function whose graph forms a straight line.

y = 2x + 5: YES y = x2 – 3: NO

No

Parent function

A family of functions is a group of functions with common characteristics. A parent function is the simplest function with these characteristics.

Pictures/Examples Quadratic one

Linear one

y=x y = x2 y= x

Slope Pictures/Examples

y

x

The ratio of the vertical change to the horizontal change.

y x y2  y1 x2  x1

rise run

“m”

“down 3, over 5” is

3  5

Slopeintercept form Pictures/Examples m b

A linear equation of a nonvertical line written as y = mx + b, where m is the slope and b is the y- intercept.

y = 3x + 2: YES y – 2 = 3x: NO

Point-slope form Pictures/Examples

A form of a linear equation, y  y1  m  x  x1  where m is the slope and  x1, y1  is a point on the line. (Holt Algebra 2 Textbook)

1 y  2  ( x  4) 2 Point: Slope:

(4,2) 1 2

Standard Form (of a line)

A form of a linear equation, Ax  By  C where A, B, and C are integers.

Pictures/Examples

5x + 6y = 30

The form this equation is in.

Inequality

A mathematical sentence that compares the values of two expressions using an inequality symbol.

Pictures/Examples

-3

-2

-1

0

1

2

3

x>1

System of equations

Two or more equations using the same variables.

Pictures/Examples

1 y x 2 1 y  x2 2

Factor(s) of a polynomial

A simplified polynomial that divides evenly into the larger given polynomial .

Pictures/Examples

x2 – 4 = (x – 2)(x + 2) (x + 2) and (x – 2) are the examples.

Parameter changes

Pictures/Examples

The resulting graph of a function when the function’s parameters are changed.

Translates right (shift it right)

“Makes it wider”

Translates left (shift it left)

“Makes it narrower”

Translates down (shift it down)

“y = 5x is steeper than y = 3x”

Translates up (shift it up)

The higher one is f(x) = x2 and the lower one is f(x) = x2 – 3.

“y = x + 7 is 2 units higher than y = x + 5”

Polynomial

A monomial or the sum or difference of two or more monomials. A quotient with a variable in the denominator is not a polynomial.

Pictures/Examples

YES

2x 3  x 2  x  9

NO

2  4x  5 2 x

2x2, 3x + 7, 28, and – 7x3 – 2 x2 + 9 are all examples.

Quadratic function

A function of the form y = ax2 + bx + c, where a  0 The graph of a quadratic function is a parabola, a U-shaped curve that opens up or down.

Pictures/Examples

y = 2x2 + 3x + 1

Quadratic equation

An equation you can write in the standard form ax2 + bx + c = 0. A quadratic equation can have two, one or no real solutions.

Pictures/Examples

ax  bx  c  0 2

x 2  9  16

Factor(s) of a polynomial

A simplified polynomial that divides evenly into the larger given polynomial .

Pictures/Examples

x2 – 4 = (x – 2)(x + 2) (x + 2) and (x – 2) are the examples.

Vertex

The highest or lowest point on a parabola. The axes of symmetry intersects the parabola at the vertex

Pictures/Examples

This point

(0, 3)

This point

(0 , – 4)

Zeroes (solutions, roots, x-intercepts) Pictures/Examples

The x-intercepts of the graph of a function. Where 5x + 2 = 0

These points

Where 2x2 + 6 =0

Perimeter

The distance around an object.

Pictures/Examples Answer would be 32 ft 6 ft

5 ft 4 ft 7 ft

What I would need to know about my farm if I want to build a fence around it.

What I need to know about my room if I want to nail crown trim the ceiling with crown moulding.

What I would need to know about my blanket if I want to sew ruffle trim around it.

Area

Pictures/Examples

The amount of space (measured in squares) inside an object.

What I would need to know about my farm if I want to plant Answer would be 100 ft2 corn all over it. What I need to know 6 ft about my room if I want to install carpet. What I would want to know 5 ft about a blanket if I want to buy 4 ft cotton material to make it. What I need to know about my wall if I want to 7 ft paint it.

Net Pictures/Examples

A two-dimensional figure that can be cut out and folded up to make a threedimensional solid.

Measure of Central Tendency Pictures/Examples

a measure of the "middle" or "expected" value of a data set

Mean, Median, and Mode are examples of this.

Measures that can describe the triangles that “balance” these data sets

Median

Pictures/Examples The answer would be 82.5: 100, 80, 80, 70, 90, 85

The number in the middle after the data has been put in order. The average of 10 and 12 in this example: 1, 10, 12, 15

One way to measure the center of the data.

Mean

The average.

Pictures/Examples The answer would be 84: 100, 80, 80, 70, 90, 85

The sum of all the data points, divided by the number of data points.

One way to measure the center of the data.

The measure used to calculate my grade in class.

Mode

The number that occurs the most in the data set.

Pictures/Examples Popularity counts. The answer would be 80: 100, 80, 80, 70, 90, 85

One way to measure the center of the data.

Range of data

The difference between the highest and lowest number in a data set.

Pictures/Examples The answer would be 30:

A useful number that indicates how spread apart your data set is. Not a way to measure the center of the data.

100, 80, 80, 70, 90, 85 Sometimes it can be a really big number or a really small number.

Right Triangle

A special triangle that has a right angle and whose sides are in the relationship a2+b2=c2, where a and b are the legs and c is the hypotenuse.

Pictures/Examples

12

13

5

N

E

W

S

Similar

Figures that are the same shape but not necessarily the same size. Their sides are in proportion.

Pictures/Examples

6 10

5

5

10

3 2

4

Venn Diagrams Pictures/Examples

Maps that are comprised of overlapping circles. The interiors of the circles symbolically represent the elements that are members of the set, while the exterior represents elements which are not members of the set A way to arrange common and uncommon characteristics between subjects.

Diameter

a diameter of a circle is any straight line segment that passes through the center of the circle and whose endpoints are on the circle

Pictures/Examples

What I need to know if I want to solve for the radius.

Circumference The distance around a circle

Pictures/Examples Sewing around the circle

What I need to know about the racetrack to figure out how many laps make a mile.

y varies “directly” with x

y = kx, where k is any number except 0. For example, y = 3x

Pictures/Examples In this example, “I make $7.50 an hour”, dollars and hours are related in this way

A line that passes through the origin

y varies “indirectly” with x Pictures/Examples

As speed decreases, time increases

k y = x , where k is any number except 0. For 3 example, y = x

The time spent exercising vs. your weight

Positive y-intercept of a graph

When the graph crosses the y-axis above y = 0.

Pictures/Examples

When b in y = mx + b is positive.

Negative y-intercept of a graph

When the graph crosses the y-axis below y = 0.

Pictures/Examples

When b in y = mx + b is negative.

y-int = -5

Volume

Pictures/Examples

How much threedimensional space it occupies

Of a prism or cylinder = Bh

Answer would be 12 Of a pyramid or cone = (1/3)Bh

Ordered Pair Pictures/Examples

(x, y)

Are used to show the position on a graph, where the "x" (horizontal) value is first, and the "y" (vertical) value is second. Written in the form (x, y)

A way to locate points on a grid or map

Total Surface Area

The sum of the surface areas of all of the faces of a solid

Pictures/Examples Of a cube = 6s2 Of a pyramid = (1/2)Pl + B What I need to know to figure out how much paint I need to paint all the sides of my mailbox.

What I need to know to figure out how much gift wrap I need.

Lateral Surface Area Pictures/Examples What I need to know to figure out how much paint I need to paint all the sides of my mailbox except the top and bottom.

Of a pyramid = (1/2)Pl

The sum of the surface areas of all of the faces of a solid, excluding the base or bases. Only the top of this cone

Only this face of the cylinder

Only the triangles in this picture

On the TAKS chart, the letter that symbolizes the area of the base of the solid.

Base Area (Big B) Pictures/Examples Of a triangular pyramid = (1/2)bh

First thing I need to know when I calculate the volume of a solid.

Only the square in this picture

The bottom and top of this rectangular prism.

Just the bottom of this cone.

Transform

Pictures/Examples

Types of this are: Translation Reflection Rotation Dilation

general term for four specific ways to manipulate the shape of a point, a line, or shape

Dilate

To make wider or larger; cause to expand

Pictures/Examples

What I would be doing if I was applying a scale factor to an object.

Scale Factor

The ratio of any two corresponding lengths in two similar geometric figures. Formula is new _ length old _ length

Pictures/Examples

Translate

moving every point a constant distance in a specified direction.

Pictures/Examples Sliding a figure or graph without changing the size or turning it.

Reflect

Pictures/Examples

Over the y-axis: (x,y) -> (-x, y)

a mapping that transforms an object into its mirror image using a line of reflection

Midpoint

the middle point of a line segment

Pictures/Examples The formula is

 x1  x2 y1  y2  ? ,  2 2   Equidistant from the ends of the segment

Endpoint

Pictures/Examples

a point at which a line segment or a ray ends

Where I begin and end when measuring a segment.

Points C, D, and M in this picture.

Point A in this picture

Horizontal

Pictures/Examples

near, on, or parallel to the horizon

A object in this direction is sometimes referred to as “flat”

Intersects at a right angle with a vertical line

Vertical

Pictures/Examples the direction aligned with the direction of the force of gravity The line test in this direction tells whether a graph is a function or not.

Direction that goes straight up and down, parallel to the yaxis of the coordinate plane

Dimensions

Pictures/Examples

What I need to know about an object before I can calculate its area, perimeter, or volume.

Same as 'measurements’ of an object

Revolution

Pictures/Examples

One complete turn or a rotation of 360°

“R” in RPM for cars

Turn around once.