Notes
Functions and Graphing
Reading Graphs
BIG QUESTION: How do you tell if a graph is a function?
A function means that for every input, there is only ONE _______________.
*A graph represents a function, if and only if it passes the
_________________________________(also called the pencil test)
-If you draw a vertical line through the graph, it does not pass through more than one
point at any given time
2. Domain and Range
*The domain of a graph is all of its ________________________ (inputs)
*The range of a graph is all of its ________________________ (outputs)
-If the graph is continuous, the domain and range will be represented as an
inequality
-If the graph is discrete (discontinuous), the domain and range will be
represented as a list
3. Zeroes
*The zeroes of a graph are where the graph crosses the ___________________.
4. x-intercepts and y-intercepts
*The intercepts of a graph are where the graph crosses the axes.
* x-intercepts cross the ____ axis
* y-intercepts cross the ____axis
5. Increasing/Decreasing
*Remember to always read a graph from ___________ to _____________
Linear
Quadratic
Reading Equations
1. Is it a function?
*An equation is a function if each ___________ (x-value) produces only one
____________ (y-value)
*If you are looking at a table, there should not be repeating _____-values with
different y-values
2. Domain and Range (Remember
)
*If given the domain of an equation, plug in each x-value to find the _____________
(y-value)
3. Zeroes
*To find the zeroes of an equation, plug in 0 for _____ and solve for 𝑥.
4. x-intercepts and y-intercepts
*To find the x-intercepts of an equation, plug in 0 for 𝑦 and solve for _______
*To find the y-intercepts of an equation, plug in 0 for 𝑥 and solve for _______
5. Function Notation
*f(x) is read “f of x”; this notation indicates that the equation is a function.
*f(x) replaces the “____” in an equation, but it means the same thing! (both represent
the output)
-If given 𝑓(#), the # in parentheses should be plugged in for the ___-value
-If given 𝑓(𝑥) = #, the equation should be set = to the number and solved for ___!
𝑦=𝑥
𝑦 = 𝑥2