AP Precalc exam

If a polar coordinate has a negative r value, what does that mean?

Go in backwards direction from what it would be if it was positive

If a polar coordinate has a negtaive theta value, what does that mean?

Go in clockwise direction instead of counter clockwise

What is the coordinate template of polar coordinates? An example?

(r[radius], theta). Example is (2, pi/2). The radius is the number of rings from the origin

Is there mutliple ways to name a polar coordinate? Yes or no and how?

Yes. By making the radius a coterminal angle and by making the raidus smaller

What is the polar coordinate for x?

rcostheta

what is the polar coordniate for y?

rsintheta

How to get polar coordinate from c coordinates?

Use r²=x²+y². It is the pythaorean formula

How to plot imaginary numbers

equation is a+bi. A is x and B is y

How to know sine or cosine for petal polar coordinates

If one petal on the y axis, its sine, if it is on the x-axis, its cosine

How to know how many petals in a petal polar coordinate graph?

Multiply the number being multiplied by theta by two

How to know if a butt polar coordinate is positive or negative

if the cosine is positive

What is a point of inflection?

Point where concavity changes

What is the leading term?

The first overall term including numbers and letters and exponents in standard position

What is the leading coefficient

The numerical number with the leading term

How to get the turning points from the degree of a polynomial?

Subtract 1 from the degree of the polynomial

What is true about even and odd functions concerning extremas?

Even functions must have a global maximum OR a global minimum but NOT BOTH. Odd functions will have NEITHER

If a is a root, what else is known in terms for the polynomial function?

It is known that a is a factor of the polynomial

What is the equation for imaginary numbers??

a+bi

What does a multiplicity of 1 mean for a factor?

It goes through the x-axis once.

What does the multiplicity of an even number mean for a factor?

The graph bounces off the x-axis

What does an odd multiplicity mean for a factor?

The graph snakes through the x-axis but onto the other side.

What does a negative coefficient mean for a polynomial graph?

The right side goes down

What is the eqution for an even number and what does it mean?

f(-x)=f(x). It means that if you change the sign on x, the y stays the same

What is the equation for odd functions and what does it mean?

g(-x)=-g(x). It means that when you change the sign of x, the sign of y changes

What is true about odd and even functions about constants?

Even functions can have constants but odd cant have constants

How to know the degree of a quadratic based on a table?

The number of differences where they are now the same

What letters are the horizontal transformations for quadratic equations and what does each one mean?

b and c are horizontal and inside the (). b is a horizontal dialation of the opposite of what b says so 1/b. c is the translation. Positive is to the left and negtaive is to the right

What letters are vertical and what does each one mean?

a and d are vertical. a is a dialation of whateevr number it is and d is a translation.

How to write the inverse for an equation?

Switch x’s and y’s. Solve for y. Switch y for x and put inverse function notation.

How to find the equation of an inverse rational equation?

Switch x’s and y’s, multiply both sides by the denominator (distribute the x). Move all Y terms to the left side and put the rest on the right. Factor out the y and divide to isolate the y. Switch y’s with x’s an put inverse function notation

How to prove if functions are inverses?

If they equal x when set equal to each other.

What is the equation for arithmetic functions? WHat does each letter mean?

a+b(n-1). A is the starting number or amount in any sequence term. b is what the equation is being increased by. 1 is the sequence number

What is the equation if you dont know the starting nymber for artihmetic?

a_n=a_k+d(n-k)

What is the euqtion for geomertic equtionbs if i dont know the startind numver

g_n=g_k(r)^n-k

What is the equation for a geometric sequence

g_n=g₁(r)^n-1

How to write exponential equation from a table?

On a graph where the x values increase by 1 and starts at 0 and the y values divide by the same thing, the a value is the initial number and the b value is the dividing number/factor. If the y values dont have the same factor initially, get the factor from the second difference through division; then do (factor)((any y value)+S)=(next y value)+S for the vertical translation but flip the sign; the second difference factor is the b value. If the x-values are not normal, do x=(subtraction difference between x-values)z+(first x value) and this is for the exponent; the x-values shift based on the answer so the a value is the new x-value

What is teh horizontal asymptote if a rational function is bottom heavy?

y=0

What is teh horizontal asymptote if a rational function is top heavy?

Oblique and do long division to find equation. Slant if the exponent difference is 1

What is teh horizontal asymptote if a rational function is middle heavy?

Fraction of top and bottom number. t/b

Whre is the y intercept of a rational function?

constants of top and bottom divided

Where are vertical asymptotes?

factors in denominator

Where are the x-intercepts?

Factors in numerator

What is a factor if its on the top and the bottom but higher multiplicity on the top?

It is a hole

WHat is a factor if it is on the top and the bottom but higher mulitplicity on the bottom

Vertical asymptote

How to know end behaviotr of a rational equation?

Looking at horizontal asymptote. Its a number if horuzontal asymptote is js a number