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!
What is slope formula
M= y2-y1/x2-x1
How do you do the rate of change when given an equation such as 3x^2 from 1 to 3
Plug-in the 1 into the equation and solve. then plug-in the 3 into the equation and solve. The solution would be the y axis to the respected x variables plugged in (the 1 and the 3). Then do the slope of both pairs
How do you algebraically find if a function is even?
A function is even if f(-x) = f(x)
So plug in -x into the X variables in the equation and if the original equation comes out then it is even
How do you algebraically find out if the function is odd?
First of all you have to find that the function is not even then you multiply the original equation by a negative one if the resulting equation then equals the result for the even calculations then it’s odd. For example, f(x)= x^3
Even: f(-x) = -x^3 <—-the wrong equation for even but the right equation for odd and also has to be identical equation to the result in the even
