Module 1 - Precalculus Slop

Question 1

In order for a function to have an inverse, it must do what?

Answer 1

It must pass the horizontal line test

Question 2

What are the steps when looking for an inverse of a function?

Answer 2

1. Switch x and y
2. Likely use an identity or a definition (what does coshx equal? etc.)
3. Look to see If u substitution can be used and then factor
4. Remember - the end goal is to isolate for y after the switch no matter how this is done!

Question 3

What is a level curve?

Answer 3

a point on the surface of a two-variable equation where z equals a constant value

Question 4

What are the steps to obtaining the formula for a level curve when the z value is given to us in the question?

Answer 4

1. insert the z value into the equation
2. isolate for y

Question 5

What does the parametric curve formula look like?

Answer 5

Question 6

What are the two properties of parametric form?

Answer 6

Orientation and starting point

Question 7

How can orientation be solved for?

Answer 7

Question 8

How can starting point be solved for?

Answer 8

Question 9

What are the steps when converting a cartesian function to parametric form?

Answer 9

1. Set either x or y equal to “t”
2. replace either the x/y value with t in the given equation
3. isolate the other variable in the equation
4. place t in x or y then the isolated equation in the other spot ->
   Ex:
   (t, t+2)

Question 10

What are the steps when converting an equation from parametric form to cartesian form? (removing parameters)

Answer 10

There are two possible methods to remove the parameters -

Method One:

1. Begin by isolating for “t” in one of the equations
2. Then insert the t equation into the y/x coordinate and simplify (be aware if the question is looking for intensive or extensive equation)

Method Two:

1. rearrange either the x or y coordinate to force the formula for the x or y to appear
2. Once it appears, insert x/y and simplify

Question 11

What is the “x” value and “y” values in polar cords

Answer 11

Question 12

What are the special formulas to convert polar to cartesian?

Answer 12

Question 13

What are the special formulas when converting cartesian to polar?

Answer 13

Question 14

What are the steps when converting a function from cartesian to polar?

Answer 14

Start with trying to find theta

1. Try to get (y/x) and replace with tan(theta)
2. Then solve for theta

If theta cannot be easily solved, then:

1. convert x’s and y’s into their corresponding r formulas
2. isolate for r

Question 15

What are the steps when converting a function from polar to parametric?

Answer 15

Question 16

What are the steps to convert a polar function to cartesian form?

Answer 16

1. look for r^2 in the equation (you can also make r^2 by multiplying by sides by r)
2. replace r^2 with x^2 + y^2
3. If r terms remain, then square both sides in order to help simplify and isolate for r