Pre-Calc Review

What’s a Function

• No repeated x values

• Passes the VLT

What’s a one-to-one function?

• no repeated X OR Y outputs

• On an FRQ, no repeated outputs

af(x)

vertical dilation

f(ax)

horizontal dilation

Axis of symmetry

-b/2a

Even multiplicity

bounce off x-axis

odd multiplicity

crosses x-axis

Even degree

same direction end behavior (think parabola)

Odd degree

opposite direction end behavior (think cubic)

bottom heavy

HA y=0

top heavy

No HA

Pythagorean Identity

cos²x + sin²x= 1

sec

1/cosx

csc

1/sinx

cot

1/tanx

sin(2x)

2sinxcosx

tan²x +1= sec²x (How did I get this?

Divide the pythagorean identity by cos²x

cot²x +1=csc²x(how to get this?)

Divide everything by sin²x

exponential function

over equally spaced inputs, the y values multiple by a factor

logarithmic function

over equally spaced inputs, the inputs are multiplied by a factor

semi-log plot

logarithmic looks linear