Chapter Sections 1.3 & 2.1-2.3 Flashcards
A graph has y axis symmetry if for every point (x,y) on the graph, ( , ) must also be on the graph
(-x,y)
A graph has x axis symmetry if for every point (x,y) on the graph, ( , ) must also be in the graph
(X,-y)
A graph has origin symmetry it for every (x,y) on the graph, ( , )must also be on the graph
(-x,-y)
How do you algebraically test for X axis symmetry?
Replace Y with -y then simplify and if original equation then it does have X axis symmetry
How do you algebraically test for Y axis symmetry
Replace X with -X ,then simplify and if original equation is an outcome then yes it does have Y axis symmetry
How do you algebraically test for original symmetry
Replace X and Y with -X and -Y then simplify and if original then yes it has original symmetry
What is the definition of a function
For each input there is one output
How do you know if a list of pairs is a function or not
If y’s repeat then it’s okay if x’s repeat then it’s not a function
For a list of pairs which parts of the pairs are the domain and which parts are the range
The X values are the domains and the y values are the range
What is set notation
{x:x = ?}
(Equal sign should be not equal to)
{x:x> ?}
Etc
What is interval notation
[ = included ( = not included
[?,?) <—– if two domains
What is the difference quotient equation?
(F(x+h) - f(x))/ h
Ex) f(x)= -3x+1
Diff quotient : -3(x+h) +1 - (-3x+1) / h
What would you do to determine the domain of: 1/x+5
X+5 is not equal (=) to 0
What would you do to determine the domain of: 1/ the square root of x+ 7
X + 7 > 0
What would you do to determine the domain of: square root of X+3
X+3 > or equal to 0
Tip to remember
Open dots means excluded and closed dots mean included on graphs
To find the y intercepts on an equation what do you do
Plug in zero for every X in the Equation
To find the x intercepts on an equation what do you do
Plug in zero for every Y variable in the equation
If it asks you if the point is on a graph what do you do?
You plug the X in the ordered pair into the x variables in the equation. If the y in the ordered pair comes out as an answer then it is on the graph
If it asks you “if f(x)= ?, what is x” what do you do
You plug in the ? For f(x) making and equation ?= x+?/x+? (Not have to be exactly like this) and solve for x! List answers in ordered pairs (x,y)
What’s the difference between location and value
Location is x in the ordered pair and value is the y-value
What are intercepts
Points at which the graph hits the y and x axis
How do you determine if a graph is even odd or neither
If the graph is symmetrical over y axis then it is even
If it is symmetrical over the origin then it is odd
If no symmetry or has x-axis symmetry then neither
What is the equation for the average rate of change
F(x)-f(c)/ x-c or slope!
