Unit 1 of Ap Pre Calc

What to do when asked to predict the value of x=7?

(aroc x 7) + y-int = answer

What has to be true for their to be a positive rate of change?

Both quantities do the same thing (increase or decrease)

What has to be true for their to be a negative rate of change?

One quantity increases while the other decreases

What is the rate of change of the Avg ROC of a linear function?

0

What is the rate of change of the Avg ROC

It changes at a linear rate (but the roc is never truly accurate)

True or False: Polynomials can divide

False

True of False: Polynomials can’t be imaginary?

True!

True or False: Polynomials can’t have negative degreees

True

What does the i for imaginary equal?

√-1

Polynomials with an ____ degree will always have a global/absolute max or min?

Even

What is a root?

x-intercept or zero

True or False: Zeros can be real and imaginary

True

Where are real zeros found?

seen on the graph

How are the imaginary zeros found?

solve through equations

How do you find the degree from the equation?

The highest degree

How do you find the number of zeros in a function?

The highest degree

How do you find whether a part of the function is odd or even multiplicity?

It’s degree

What does the odd multiplicity zeros on the graph mean? do

goes through the graph

What does the even multiplicity zeros on the graph?

bounces off the graph

How can you tell if a function is even?

f(-x)=f(x) or when the function is reflected off the y-axis, it looks the same

How can you tell if a function is odd?

f(=x)=-f(x) or if rotated on the origin 180^o it remains the same

What is the top of the limit notation?

lim f(x) = ♾/ -♾

What is the bottom of the limit notation?

x → ♾/-♾

What does x → 0^- do?

end behavior as it comes in from the left

What does x → 0⁺ do?

end behavior as it comes in from the right

What is the limit notation of a function with a pos leading coefficient and an even degree?

♾,♾

What is the limit notation of a function with a pos leading coefficient and an odd degree?

♾,-♾

What is the limit notation of a function with a negative leading coefficient and an odd degree?

-♾,-♾

What is the limit notation of a function with a negative leading coefficient and an even degree?

-♾, ♾

If the degree is higher on the bottom of a rational function, the limit is _

0

If the degree is the same on the top and the bottom of a rational function, the limit is _

the ratio of coefficients

If the degree is higher on the top of the rational function, the limit is _______

dependent on an infinity table

If the degree is higher on the top and has a positive leading coefficient, the limit pair is…

-♾, ♾

If the degree is higher on the top and has a negative leading coefficient, the limit pair is…

♾, -♾

Where to find the zeros of a rational function

The zeros of the top of the function

Where to find the vertical asym of a rational function?

The zeros of the bottom of the fraction

f(x)= ± a (bx±c)+d what does a do?

1. vertical dilation

2. vertical reflection if negative

3. 0<a: shrink

4. 0>a: stretch

f(x)= ± a (bx±c)+d what does b do?

1. horizonal dilation

2. horizontal reflection

f(x)= ± a (bx±c)+d what does c do?

left or right c

f(x)= ± a (bx±c)+d what does d do?

up or down d

What function should be used if the problem mentions a constant roc?

A linear function

What function should be used if the problem mentions the ROC shifting, one distinct min or max

Quadratic

What function should be used if the problem mentions volume?

cubic

What function should be used if the problem mentions different characteristics over different intervals?

Piecewise/multiple functions?

If a residual plot is scattered, the linear model is appropriate/not appropriate

appropriate

If a residual plot has a pattern, the linear model is appropriate/not appropriate

not appropriate