Algebra II Flashcards
A set of ordered pairs can be shown in a ______, _______, _______, or expressed as an ______.
- Graph
- Table of values
- Mapping diagram
- Equation
The set of x-values is called the _______ and the set of y-values is called the _______.
- Domain
- Range
A relation with distinct points is called _______. A relation with connected lines or curvees is called _______.
- Discrete
- Continuous
Rules for domain and range
- Order from least to greatest
- No repeats
- In brackets {}
Function definition and example:
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)}
Vertical line test:
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))
Continuous examples:
- 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.
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)
y = 21 (-7, 21)
y = 2 (1/2, 2)
y = -37 (-3, -37)
y = -40 (3, -40) (-1, -40)
Input, output
When points on a graph lie along a straight line, it is called a _______
linear function
Linear relations can be represented by an _______, for example, the equation of this graph can be written as _______
equations/functions
Standard form: x + y = 8
Slope-intercept form: y = -x + 8
What is the difference between a liner equation and a nonlinear equation?
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
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
linear function
The point at which the line intersects the x-axis is called _______
The point at which the line intersects the y-axis is called _______
x-intercept
y-intercept
The x-intercept is also referred to as _______, _______, or _______ to the equation
Solutions
Roots
Zeros
To find the x-intercept of an equation, _______ and solve for _______.
To find the y-intercept of an equation, _______ and solve for _______
Cover up y
x
Cover up x
y
x-intercepts and y-intercepts can be written as a _______ or an _______
graph point
equation
To find slope always do _______
vertical or rise first then do horizontal
What is slope in the slope form equation (y = mx + b)?
m
_______a ratio that shows how one variable changes with respect to another.
On a linear graph, this is called the _______ of the line
Fraction/composition
slope
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
ratio
y-values
x-values
constant
Slope is written as a _______ in _______. Variable for slope _______.
Fraction
Rise(y)/run(x)
m
Types of slopes:
Positive:
Negative:
Zero:
Undefined:
Rise to the right
Fall to the right
Horizontal line 0/# = 0
Vertical line #/0 = undefined
Slope formula:
m = y2 - y1/x2 - x1
Linear equations are often written in slope-intercept form:
y = mx + b or f(x) = mx + b
(Where m is the slope and b is the y-intercept)
