Pre-Calc Review

Definition

100

a_nxⁿ+a_n-1x^n-1+...a₁x+a₀ where a is real numbers, n is a positive whole number, and the domain is (-infinity, infinity)

What is a polynomial?

200

A function of the form f(x)=Ca^x where a>0, a cannot be 1, and C cannot be zero

What is an exponential function?

300

If the functions satisfy these conditions (f(g(x))=x and g(f(x))=x

What is an inverse?

400

y=log_b(x) is equivalent to b^y=x

What is a log function?

500

Approximately 2.718281... 

What is e? Or What is the natural number

Polynomial Functions

100

(0,y) and (x,0)

What are intercepts?

Best response: What are x and y intercepts

200

The highest power of x that shows up in a polynomial

What is the degree?

300

As x approaches infinity, f(x) approaches negative infinity. 

As x approaches negative infinity, f(x) approaches negative infinity

What is end behavior?

Best: What is an even degree and negative leading coefficient end behavior?

400

f(x)=(x-2)(x+1)(x-3)⁴

x=2,-1,3

mult=1,1,4

What is multiplicity?

500

Need degree, x-intercepts, y-intercept

What do you need to graph a sketch of a polynomial?

Or

What do you need to make an equation of a polynomial function?

Exponential Functions

100

(0,1) and (1,a)

What are values always on exponential functions that haven't been shifted?

200

Given a function f(x), if as x approaches infinity or as x approaches negative infinity, the function f(x) approaches c where c is a real number, then y=c

What is a horizontal asymptote?

300

If a^x=a^y, then x=y

(a^x)^y=a^xy

a^xa^y=a^x+y

What are exponential rules(facts)?

400

2^-x=2^x+2

the point (-1,2)

What is the point of intersection?

500

f(x)=2^x+3

Answer:y=3

What is the horizontal asymptote of f(x)? 

Inverse Functions

100

if for every x and y in its domain, if f(x)=f(y), then x=y

What is a one to one function?

200

The graphic way to check if something is one to one

What is the horizontal line test?

300

Replace f(x) with y

switch x and y in equation 

solve for y. The result is the inverse of f

What is the algebraic way of finding the inverse?

Also: What are the steps to finding an inverse? 

400

(b,a) is the reflection of the point(a,b) across the line y=x

What is the graphic way of finding an inverse?

500

The only way that f(x)=x² has an inverse is if we do this

What is restricting the domain?

Log Functions

100

log_b(b^x)=x

b^log_b^(x)=x

log_b(xy)=log_b(x)+log_b(y)

What are important log rules?

200

(1,0) and (b,1)

What are points on non-transformed log functions?

300

y=log₃(5x+3)-2

x=-3/5

What is the vertical asymptote?

400

ln(x)

What is the log of base e?

500

log(x)

b=10

What is the base of the log?