Chapter Sections 1.3 & 2.1-2.3

Question 0

A graph has y axis symmetry if for every point (x,y) on the graph, ( , ) must also be on the graph

Answer 0

(-x,y)

Question 1

A graph has x axis symmetry if for every point (x,y) on the graph, ( , ) must also be in the graph

Answer 1

(X,-y)

Question 2

A graph has origin symmetry it for every (x,y) on the graph, ( , )must also be on the graph

Answer 2

(-x,-y)

Question 3

How do you algebraically test for X axis symmetry?

Answer 3

Replace Y with -y then simplify and if original equation then it does have X axis symmetry

Question 4

How do you algebraically test for Y axis symmetry

Answer 4

Replace X with -X ,then simplify and if original equation is an outcome then yes it does have Y axis symmetry

Question 5

How do you algebraically test for original symmetry

Answer 5

Replace X and Y with -X and -Y then simplify and if original then yes it has original symmetry

Question 6

What is the definition of a function

Answer 6

For each input there is one output

Question 7

How do you know if a list of pairs is a function or not

Answer 7

If y’s repeat then it’s okay if x’s repeat then it’s not a function

Question 8

For a list of pairs which parts of the pairs are the domain and which parts are the range

Answer 8

The X values are the domains and the y values are the range

Question 9

What is set notation

Answer 9

{x:x = ?}
(Equal sign should be not equal to)
{x:x> ?}
Etc

Question 10

What is interval notation

Answer 10

[ = included
( = not included 

[?,?) <—– if two domains

Question 11

What is the difference quotient equation?

Answer 11

(F(x+h) - f(x))/ h
Ex) f(x)= -3x+1
Diff quotient : -3(x+h) +1 - (-3x+1) / h

Question 12

What would you do to determine the domain of: 1/x+5

Answer 12

X+5 is not equal (=) to 0

Question 13

What would you do to determine the domain of: 1/ the square root of x+ 7

Answer 13

X + 7 > 0

Question 14

What would you do to determine the domain of: square root of X+3

Answer 14

X+3 > or equal to 0

Question 15

Tip to remember

Answer 15

Open dots means excluded and closed dots mean included on graphs

Question 16

To find the y intercepts on an equation what do you do

Answer 16

Plug in zero for every X in the Equation

Question 17

To find the x intercepts on an equation what do you do

Answer 17

Plug in zero for every Y variable in the equation

Question 18

If it asks you if the point is on a graph what do you do?

Answer 18

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

Question 19

If it asks you “if f(x)= ?, what is x” what do you do

Answer 19

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)

Question 20

What’s the difference between location and value

Answer 20

Location is x in the ordered pair and value is the y-value

Question 21

What are intercepts

Answer 21

Points at which the graph hits the y and x axis

Question 22

How do you determine if a graph is even odd or neither

Answer 22

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

Question 23

What is the equation for the average rate of change

Answer 23

F(x)-f(c)/ x-c or slope!

Question 24

What is slope formula

Answer 24

M= y2-y1/x2-x1

Question 25

How do you do the rate of change when given an equation such as 3x^2 from 1 to 3

Answer 25

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

Question 26

How do you algebraically find if a function is even?

Answer 26

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

Question 27

How do you algebraically find out if the function is odd?

Answer 27

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