ap pre cal unit 1

(1 difference)

linear

(2 difference)

quadratic

(3 difference)

cubic

graph y=0 → 2nd trace → intersect → 1,2,3 intersect

Restricted Domain

graph y = 0 → 2nd trace → max

restricted range

y2-y1

---

x2 - x1

Average rate of change

stat → edit

data table

2nd y= → zoom → 6

see graph from data

stat → ___ reg → calculate

equation of the regression curve

stat → cal __ → store reg → vars → y-vars → functions → y= → graph

vars → y-vars → function → y1 (x)

find variable

y = k/x

inverse proportional

constant of property =

k

if the bottom degree is bigger, the HA is

y = 0

if the top degree is bigger, the HA is

HA = none

if the degrees are the same, the HA is

a/b

when the numerator is factored and isn’t cancelled in a function

zero

When the numerator and denominator cancel out a factor

hole

denominator factors that didn’t cancel

vertical asymptote

when 0 is plugged into the equation for the variable

y-intercept

domain

factors of the denominator

f(x) + d

Vertical translation up d units

f(x) - d

vertical translation down d units

f(x + c)

Horizontal translation left d units

f(x-c)

Horizontal translation right c units

-f(x)

Reflection over x-axis

f(-x)

Reflection over y-axis

af(x); |a| > 1

Vertical stretch; (x,y) ➡ (x, ay)

af(x); 0 < |a| < 1

vertical compression; (x,y) ➡ (x, ay

f(bx); |b| > 1

horizontal compression; (x,y) ➡ (x/b , y)

f(bx); 0 < |b| < 1

Horizontal stretch (x,y) ➡ (x/b , y)

if the denominator degree is higher than the top degree and can be divided

slant asymptote

Even + Negative

Left: Right

lim p(x) = ꝏ lim p(x) = ꝏ

x → ꝏ x → ꝏ

Odd

over (0,0)

Even

over x=0

x is the ____ variable

independent

y is the _______ variable

dependent

even and positive extrema

global minimum

even and negative extrema

global maximum

Odd and Positive

Left: Right

lim p(x) = -ꝏ lim p(x) = ꝏ

x → -ꝏ x → ꝏ

Odd and Negative

Left: Right

lim p(x) = ꝏ lim p(x) = -ꝏ

x → -ꝏ x → ꝏ

Even and Negative

Left: Right

lim p(x) = -ꝏ lim p(x) = -ꝏ

x →- ꝏ x → ꝏ

positive rate of change

one quantity increases/decreases, the other does the same

negative rate of change

one quantity increases and one decreases