Pre-Calc Exam

Domain when inside log func is (-x)

(-inf, 0), start with neg inf

(-x) transformation

reflect over y axis

finding parent pts in log func

rewrite the base into exponential form

y=log2(x)

= 2y

the point u plug in goes first

What is the domain rule for a logarithm?

Its input must be positive: set the argument \(>0\). If there are multiple logs, all conditions must hold.

What if the same log appears on both sides?

\(\log_b M=\log_b N\) means \(M=N\), provided both inputs are positive.

What is the solve-and-check routine for log equations?

Find the domain, use log rules, solve, then reject any candidate outside the original domain.

What are two parent points for \(y=\log_bx\)?

\((1,0)\) and \((b,1)\), since \(\log_b1=0\) and \(\log_bb=1\).

polynomial domain

always (neg inf, pos inf)

x- intercepts polynomal func

set f(x) = 0

y-intercepts polynomial

x=0

end behavior polynomal

leading term

polynomial bounce

use mulplicity to see if bounce or not

exponential graph domain

domain is always neg inf, pos inf

exponential graph domain

y=k (last number being added)

Points in exponential

parent function

Log graph domain

find by rqurining logs input to be positive

asymtopte for log graph

x=, vertical asymtope (find by whats being subtratced inside the parenthesis)

Range log graph

(neg inf, pos inf)

Finding pts on log graph

base^y = x

Inverse graphs pts

(a,b) goes to (b,a)

Inverse graphs domain + range

swap with non invcerse

Horizontal asy for inverse graph

becoems vertical (becomes horizontal if parent is vertical also)