Topic 1: Relations and Functions
Definitions:
Relation- a set of input and output values, usually represented as ordered pairs
Function-special type of relation in which each element of the domain is paired with exactly one element of the range
Domain- x values
Range- y values
Vertical Line Test- slide a vertical line across a graph, as long as it touches one part of the graph at every spot then the graph is a function
Function Notation- another name for y =, f(x) (we say f of x), x is the input value
Helpful Hints:
Video Examples:
Is the Relation a Function?
Relation- a set of input and output values, usually represented as ordered pairs
Function-special type of relation in which each element of the domain is paired with exactly one element of the range
Domain- x values
Range- y values
Vertical Line Test- slide a vertical line across a graph, as long as it touches one part of the graph at every spot then the graph is a function
Function Notation- another name for y =, f(x) (we say f of x), x is the input value
Helpful Hints:
- Domain- how far left to how far right
- Range- How low to how high
Video Examples:
Is the Relation a Function?
Domain and Range
Evaluating Functions
Topic 2: Linear Equations
Definitions:
Linear Function- highest exponent is 1 and there are no other operations besides addition, subtraction, multiplication or division
Standard Form - Ax + By = C, where A,B, and C are integers whose greatest common factor is 1, (A cannot be negative)
Helpful Hints:
Video Examples:
Writing Equations in Standard Form from Slope-Intercept Form
Linear Function- highest exponent is 1 and there are no other operations besides addition, subtraction, multiplication or division
Standard Form - Ax + By = C, where A,B, and C are integers whose greatest common factor is 1, (A cannot be negative)
Helpful Hints:
- Linear function can be written as f(x) = mx +b ...essentially y = mx +b
- To help get rid of fractions for standard form, multiply by the denominator
Video Examples:
Writing Equations in Standard Form from Slope-Intercept Form
Topic 3: Slope
Definitions:
Slope - ratio of change in y over change in x
Helpful Hints:
Video Examples:
Finding the Slope From a Graph
Slope - ratio of change in y over change in x
Helpful Hints:
- slope formula (y2-y1)/(x2-x1)
Video Examples:
Finding the Slope From a Graph
Finding Slope From Two Points
Topic 4: Writing Equations of Lines
Definitions:
Slope Intercept Form- y = mx +b
Standard Form - Ax + By = C
Slope Formula - (y2-y1)/(x2-x1)
Point Slope Form - (y - y1) = m(x -x1)
Helpful Hints:
Video Examples:
Writing Equations of Lines
Slope Intercept Form- y = mx +b
Standard Form - Ax + By = C
Slope Formula - (y2-y1)/(x2-x1)
Point Slope Form - (y - y1) = m(x -x1)
Helpful Hints:
- PAY ATTENTION TO DETAILS
Video Examples:
Writing Equations of Lines
Topic 5: Special Functions
Definitions:
Step Function - special type of function whose graph is a series of line segments
Greatest Integer Function - notation: f(x) = [[x]] means the greatest integer less than or equal to x
Constant Function - f(x) = b, this will always be a horizontal line at whatever number b is
Identity Function - f(x) = x, slope is 1 and the y-intercept is 0
Absolute Value Function - f(x) = |x|, makes the shape of a V
Piecewise Function - a function that is written using two or more expressions
Helpful Hints:
Video Examples:
Constant Function
Step Function - special type of function whose graph is a series of line segments
Greatest Integer Function - notation: f(x) = [[x]] means the greatest integer less than or equal to x
Constant Function - f(x) = b, this will always be a horizontal line at whatever number b is
Identity Function - f(x) = x, slope is 1 and the y-intercept is 0
Absolute Value Function - f(x) = |x|, makes the shape of a V
Piecewise Function - a function that is written using two or more expressions
Helpful Hints:
- All parent functions act the same! (horizontal movement with the x), vertical movement with the "c" or y-intercept value, flipped if a is negative and stretched or skewed based on the value of a
- If you get stuck make a table and then graph!
Video Examples:
Constant Function
Identity Function
Absolute Value Function
Piecewise Function
Greatest Integer Function
Transformations of Graphs
Topic 6: Graphing Inequalities
Helpful Hints:
Video Examples:
Graphing Linear Inequalities
- Less than and greater than have dashed/dotted lines, less than or equal to and greater than or equal to have solid lines
- Less thans shade below, greater thans shade above
- If you replace the inequality symbol with an = sign this represents your boundary line
Video Examples:
Graphing Linear Inequalities
Topic 7: Midpoint and Distance Formulas
Helpful Hints:
Video Examples:
Midpoint and Distance Formula
- Midpoint is the average of the x values of the endpoints and the average of the y values of the end points. The answer is a point.
- With the distance formula you must make sure you use parenthesis. Pay attention to details!
Video Examples:
Midpoint and Distance Formula