Everything Flashcards

1
Q

How can you tell if a graph of a relation and it’s inverse are a function?

A

Do a vertical line test to the relation to make sure no two points are the same
Do a horizontal line test to the relation to make sure no two points are the same for the inverse

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2
Q

How do yoy algebraically and graphically find the inverse of a function?

A

Algebraically- switch X and Y in the function then isolate y

Graphically- switch the X and y points on the table of values

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3
Q

What is the domain and range for a standard radical equation?
Y= root X

A

X greater than or equal to 0

Y “

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4
Q

What happens to the X and Y values of a function when you square root the right side?

A

X stays the same

Y gets square rooted

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5
Q

What is the difference in domain and ranges between x^2-9 and root x^2-9?

A

First one- X E R
Y>or equal to -9

Second one- X>orequal to 3 Xor equal to 0

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6
Q

How do you solve a radical function graphically?

A

Isolate the radical and graph the two functions on either side of the equal sign
(Use algebraically to check)

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7
Q

What must be included when creating a normal function graph?

A

Table of values

Domain and range

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8
Q

What must be included when creating a radical function graph?

A

Table of values

Domain and range

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9
Q

When long dividing and the remainder ends up being zero, what does that mean?

A

It means what you divided the function by is a factor

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10
Q

What can you only divide by in order to use synthetic division?

A

A binomial (X-2)

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11
Q

What is the factor theorem?

A

It is when you insert a binomials number as X into what you’re dividing it by to see if it’s a factor.
If it results in 0 it is a factor

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12
Q

What do you include when creating a graph of a polynomial functions?

A
Degree
Leading coefficient sign
Quadrants it goes to
Y intercept
Zeros/multiplicity/behaviour chart
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13
Q

What should you do when asked to graph a polynomial equation?

A

Use synthetic division to simplify it to binomials then create a zeros chart and just graph it

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14
Q

What are the three things rational functions cannot have?

A
  1. Denominators cannot equal zero
  2. No common factors can exist
  3. No negative exponents in denominator
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15
Q

What must you include when creating a graph of a rational function?

A
Vertical asymptote 
Horizontal asymptote
X intercepts
Y intercepts
Sign analysis
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16
Q

How do u find vertical asymptote of rational functions?

A

Make Y equal to 0/1 and cross multiply

17
Q

How do you find the horizontal asymptote of the numerator is:

  • equal to the denominator
  • less than the denominator
  • greater than the denominator
A

Equal: the ratios of the two leading coefficients will be the asymptote
Less than: the asymptote is 0
Greater than: use long division and put the denominator on the outside and divide to find asymptote

18
Q

What is the difference between a point of discontinuity and a vertical asymptote in the denominator?

A

POD occurs when two binomials cancel eachother out and give you the X value of the POD
Vertical asymptote is just a binomial left alone in the denominator

Always check for POD first!!

19
Q

What is the formula for converting radians to degrees?

A

180/pie = degrees / radians

20
Q

What is the radius for the unit circle?

A

1

21
Q

How do you find cot 160?

A

Tan 160

Then go X to the power of -1 on calculator

22
Q

How to find cot ø= 160?

A

Tan-1(1/160)

23
Q

What do you need to include when creating a graph of cosine, sine, and tan?

A

Table of values
Domain and range
Amplitude
Period length

24
Q

When cancelling opposites where do you put the -1?

A

On the top only

25
Q

What do you include when creating a graph of an exponential function?

A
Table of values
Domain and range
X-intercepts 
Y-intercepts
Increasing or decreasing
Horizontal asymptote
26
Q

What do you include when creating the graph of a logarithm?

A
Table of values 
Increasing or decreasing
X and y int
Vertical asymptote 
Domain and range
27
Q

How do you find the inverse of a quadratic equation?

A

Complete the square then switch X and y

28
Q

What are integral zeros?

A

The factors of the constant of a polynomial

Possible factors of it

29
Q

When would you use combinations instead of permutations?

A

When they use the words: groups, committees, sets, cards