Algebra II

Question 1

A set of ordered pairs can be shown in a ______, _______, _______, or expressed as an ______.

Answer 1

1. Graph
2. Table of values
3. Mapping diagram
4. Equation

Question 2

The set of x-values is called the _______ and the set of y-values is called the _______.

Answer 2

1. Domain
2. Range

Question 3

A relation with distinct points is called _______. A relation with connected lines or curvees is called _______.

Answer 3

1. Discrete
2. Continuous

Question 4

Rules for domain and range

Answer 4

1. Order from least to greatest
2. No repeats
3. In brackets {}

Question 5

Function definition and example:

Answer 5

A relation in which each element of the domain is paired with exactly one element of the range.

Function:
{(0, 1),(-5, 2), (6, -2), (5, 7)}

NOT a function:
{(-7, 2), (6, -1), (6, 2), (-3, 9)}

Question 6

Vertical line test:

Answer 6

In order to be a function, a vertical line cannot pass through more than one point in the relation. (This means the input (x-value) would have more than one output (y-value) and would not satisfy the definition to have one input and one output…(x,y))

Question 7

Continuous examples:

Answer 7

• For domain, scan your pencil left to right and Identify the x-values in which you are “touching” the graph.
• For range, scan your pencil down and up and identify the y-values in which you are “touching” the graph.

Question 8

Given:

f(x) = -5x -14

g(x) = -x^2 + 9x -1

h(x) = 5/x + 2

Evaluate:

f(-7) h(1/2) g(-3) f(3) + g(-1)

Answer 8

y = 21 (-7, 21)

y = 2 (1/2, 2)

y = -37 (-3, -37)

y = -40 (3, -40) (-1, -40)

Input, output

Question 9

When points on a graph lie along a straight line, it is called a _______

Answer 9

linear function

Question 10

Linear relations can be represented by an _______, for example, the equation of this graph can be written as _______

Answer 10

equations/functions

Standard form: x + y = 8

Slope-intercept form: y = -x + 8

Question 11

What is the difference between a liner equation and a nonlinear equation?

Answer 11

A linear equation has only x^1 and/or y^1, but not xy, divided x or y’s, x^2 or y^2, or square roots such as nonlinear equations have

Question 12

A _______ is a function with ordered pairs that satisfy a linear equation. Any linear function can be written in the form f(x) = max + b, where m and b are real numbers

Answer 12

linear function

Question 13

The point at which the line intersects the x-axis is called _______

The point at which the line intersects the y-axis is called _______

Answer 13

x-intercept

y-intercept

Question 14

The x-intercept is also referred to as _______, _______, or _______ to the equation

Answer 14

Solutions
Roots
Zeros

Question 15

To find the x-intercept of an equation, _______ and solve for _______.

To find the y-intercept of an equation, _______ and solve for _______

Answer 15

Cover up y
x

Cover up x
y

Question 16

x-intercepts and y-intercepts can be written as a _______ or an _______

Answer 16

graph point

equation

Question 17

To find slope always do _______

Answer 17

vertical or rise first then do horizontal

Question 18

What is slope in the slope form equation (y = mx + b)?

Answer 18

m

Question 19

_______a ratio that shows how one variable changes with respect to another.

On a linear graph, this is called the _______ of the line

Answer 19

Fraction/composition

slope

Question 20

Slope is written as a _______ of the vertical change (_______) to the horizontal change (_______) between any 2 points on a line

This remains _______ for any 2 points of the same line

Answer 20

ratio
y-values
x-values

constant

Question 21

Slope is written as a _______ in _______. Variable for slope _______.

Answer 21

Fraction

Rise(y)/run(x)

m

Question 22

Types of slopes:

Positive:

Negative:

Zero:

Undefined:

Answer 22

Rise to the right

Fall to the right

Horizontal line 0/# = 0

Vertical line #/0 = undefined

Question 23

Slope formula:

Answer 23

m = y2 - y1/x2 - x1

Question 24

Linear equations are often written in slope-intercept form:

Answer 24

y = mx + b or f(x) = mx + b

(Where m is the slope and b is the y-intercept)

Question 25

To change from standard form to slope-intercept form?

Answer 25

-A/B or move the A to the other side and divide all of the numbers by the B coefficient

Question 26

To write a linear equation given the slope of the line (m), and a point that passes through (x1, y1), use the point-slope formula:

Answer 26

y - y1 = m(x - x1)

Question 27

Slope intercept for undefined is _______

Slope intercept for 0 is _______

Answer 27

x = #

y = #

Question 28

To write a linear equation given two points (x1, y1) and (x2, y2) use the _______ followed by the _______

Answer 28

Slope formula

Point slope formula

Question 29

Writing parallel and perpendicular equations. What is this?

Answer 29

Given an equation, you must create another equation that is either parallel or perpendicular to this line, passes through a certain points.

Parallel equations have same slopes

Perpendicular equations have opposite reciprocal slopes

Question 30

A piecewise function is _______

Answer 30

a function defined by 2 or more equations, or “pieces,” that apply to different parts of the domain.

Piecewise functions’ equations can include linear, absolute value, quadratic, or any other type of function. Therefore, there is no parent function for piecewise functions.

Example: f(x) = {x - 2, if x ≤ 0
{2x + 1, if x > 0

Question 31

What is a parent function?

Answer 31

the simplest form of any function family, in which it preserves the definition of the entire family.

Question 32

What is a function?

Answer 32

an equation for which any x that can be plugged into the equation will yield exactly one y out of the equation

Question 33

What is a function family?

Answer 33

a group of functions with the same degree and that look the same, even with different numbers

Question 34

An _______ on a graph means that the value is _______, and a _______ means that the value is _______

Answer 34

Open circle

Not included

Closed circle

Included

Question 35

When there is no value of y, given the x, then it’s _______

Answer 35

undefined

Question 36

Use a graph to evaluate f (x) given the _______

Answer 36

values

Question 37

When simplifying radicals, the root applies to every _______

Apply radical rule:

Answer 37

item under the radical

n^√ab = n^√a x n^√b

Question 38

When graphing linear equations, graph what first?

Answer 38

b

Question 39

Linear inequality is similar to a linear equation, but _______

Answer 39

uses an inequality symbol

Question 40

What is the solution to a Linear Inequality

Answer 40

All of the ordered pairs that make the inequality true