Unit 3a Calculus Flashcards
f(x) = c is called and looks like what?
f(x) = x is called what?
f(x) = x^2 is called what?
f(x) = x^3 is called what?
f(x) = x^4 is called what?
f(x) = x^5 is called what?
constant horizontal line
Linear
Quadratic
Cubic
Quartic
Quintic
A. If a function has an even power then it has symmetry with respect to the
B. And if it has an odd power then it has symmetry with respect to the
A. y axis
B. orgin
a. What does it mean if the lead coefficient is positive?
b. and negative?
c. What is this used for most commonly?
a. If positive the right most end goes up
b. If negative the right most end goes down
c. Sketching graphs and end behavior THIS APPLYS TO POLYNOMIAL FUNCTIONS TOO
a. What does it mean if the power is even?
b. and odd?
c. What is this used for most commonly?
a. Even the left end goes in the same direction as the right one
b. Odd the left most end goes in the opposite direction as the right most one
c. Sketching graphs and end behavior THIS APPLYS TO POLYNOMIAL FUNCTIONS TOO
What does f(x) = x^-1 equal
What does this graph look like
1/x
Its the two L looking things that never touch the x or y axis
a. when you have a thing that looks like f(x) = x^n/m what does it also look like?
b. If n is even what is the domain?
c. If its odd?
REMEMBER THESE RULES ONLY APPLY TO PROBLEMS LIKE THIS
a. nth root of x ^m
for ex it would be x^3/2 -> the cubed root of x^2
b. x is greater then or equal to 0
c. if odd both range and domain are all real numbers
a. What is a turning point?
b. What makes one a relative max or a relative min?
a. the point where a polynomial function begins to change direction
b. If the turning point is higher than any nearby point its called a relative max, if its lower then any nearby point its called a relative min.
For Polynomial Functions finding out Domain and Range
A. What is Domain?
b. If degree is even what is R c. if its odd what is R
a. its always all real numbers
b. if the leading coefficient is pos then its y is greater then or equal to …
if the leading coefficient is negative then its y is less then or equal to …
c. all real numbers
a. For multiplicity if it’s even what does that mean?
b. if its odd?
a. tangent
b. cross
For synthetic division
a.if your dividing by x-2 what do you put in the box?
b. and if you’re dividing by x+ 2?
c. The last column in synthetic division represents what?
a. 2
b. -2
c. the remainder
For Remainder theorem (or synthetic substitution)
a. if c= -3 what do you put in the box?
b. so you are dividing by c = -3 using synthetic division how do you know what f(-3) = ?
a. -3
b. it equals the remainder which is whatever is in the last column
For Factor theorem
how do you determine which binomials are factors of the given function?
you use synthetic division to divide the function by each of the binomials given, they are factors if the remainder is 0. You know the remainder is 0 if you get 0 in the last column
THERE CAN BE MORE THEN ONE ANSWER
