Everything Flashcards
How can you tell if a graph of a relation and it’s inverse are a function?
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
How do yoy algebraically and graphically find the inverse of a function?
Algebraically- switch X and Y in the function then isolate y
Graphically- switch the X and y points on the table of values
What is the domain and range for a standard radical equation?
Y= root X
X greater than or equal to 0
Y “
What happens to the X and Y values of a function when you square root the right side?
X stays the same
Y gets square rooted
What is the difference in domain and ranges between x^2-9 and root x^2-9?
First one- X E R
Y>or equal to -9
Second one- X>orequal to 3 Xor equal to 0
How do you solve a radical function graphically?
Isolate the radical and graph the two functions on either side of the equal sign
(Use algebraically to check)
What must be included when creating a normal function graph?
Table of values
Domain and range
What must be included when creating a radical function graph?
Table of values
Domain and range
When long dividing and the remainder ends up being zero, what does that mean?
It means what you divided the function by is a factor
What can you only divide by in order to use synthetic division?
A binomial (X-2)
What is the factor theorem?
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
What do you include when creating a graph of a polynomial functions?
Degree Leading coefficient sign Quadrants it goes to Y intercept Zeros/multiplicity/behaviour chart
What should you do when asked to graph a polynomial equation?
Use synthetic division to simplify it to binomials then create a zeros chart and just graph it
What are the three things rational functions cannot have?
- Denominators cannot equal zero
- No common factors can exist
- No negative exponents in denominator
What must you include when creating a graph of a rational function?
Vertical asymptote Horizontal asymptote X intercepts Y intercepts Sign analysis
How do u find vertical asymptote of rational functions?
Make Y equal to 0/1 and cross multiply
How do you find the horizontal asymptote of the numerator is:
- equal to the denominator
- less than the denominator
- greater than the denominator
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
What is the difference between a point of discontinuity and a vertical asymptote in the denominator?
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!!
What is the formula for converting radians to degrees?
180/pie = degrees / radians
What is the radius for the unit circle?
1
How do you find cot 160?
Tan 160
Then go X to the power of -1 on calculator
How to find cot ø= 160?
Tan-1(1/160)
What do you need to include when creating a graph of cosine, sine, and tan?
Table of values
Domain and range
Amplitude
Period length
When cancelling opposites where do you put the -1?
On the top only
