Download Prerequisite Skills Solving for x with absolute values Get rid of the

Prerequisite Skills
A. Solving for x with absolute values
 Get rid of the absolute value signs
by
1. setting everything within
absolute value to the opposite
2. keeping the original equation
 Solve per usual
B. Simplifying with square roots in the
denominator
 Multiply the top and bottom by the
square root on the bottom
 The square root number is no
longer a square root and becomes
the “normal” form
 Reduce square roots to simplest
form
 Solve per usual
Chapter One Skills
A. Finding the formula for f^-1(x)
 Switch the x and y values and solve per
usual
B. Altering graphs
If f(x) is a function…
 f(x)-1  graph is shifted down one unit
 f(x)+1  graph is shifted up one unit
 f(x-1)  graph is shifted right one unit
 f(x+1)  graph is shifted left one unit
 f(-x)  graph is reflected across the xaxis
C. Odd and Even functions
 A parabola is an even function
 A curve is an odd function
 A negative function will be flipped over
 A positive function is “normal”
D. Function Inception XD
 For (f o g)(x), plug in the “g” equation
in for x in the f equation

For (fg)(x) multiply the f equation by
the g equation
Chapter Two Skills
A. Writing linear equations to satisfy given
conditions
 Find the slope of the line using (y2y1)/(x2-x1)
 Plug the in the slope and a coordinate
pair into the equation y-y1=m(x-x1)
 Solve as per usual
B. Finding the vertex and axis of a graph
 If not in quadratic form, unfoil
 Find “h” with –(b/2a)  THIS IS THE
AXIS!
 Plug in “h” for all “x” values in the
equation and solve to find “k”
 (h,k) is the vertex of the parabola
C. Writing an equation for the quadratic function
to satisfy a given vertex and point
 Plug in the vertex values for h and k.
y=a(x-h)+k
 Plug in x and y values to solve for a
 Plug in a into first equation
D. Remainder Theorem
 If you plug the dividend into the divisor,
the solution will be the remainder for
the quotient
E. Factor Theorem
 If you plug in the x value into the
equation and the solution is zero, the
first polynomial is the factor of the
second
F. Qudratic Equation
G. Completing the square
 Take middle term and divide by 2
 Square the quotient above
 Take out the middle equation, add the
squared thing to both sides
 Since the left side is to the second
power, take the square root of both
sides
H. When Finding the Real Zeros of a Function…
 An= based off of the leading coefficient
 Ao= based off of the last number
 Find the factors of AN and AO. Use the
factors of AO over AN to find possible
zeros.
 Once you find a zero, do synthetic
division with that number, rewrite the
equation as a quadratic, and solve with
the quadratic formula.
 To write in linear factorization, do (xn)…
I. Finding Asymptotes and Intercepts
 Y-Intercept: plug in 0 for x-values and
solve
 X-intercept: set the numerator to zero
and solve
 Vertical Asymptote: set the bottom to
zero

Horizontal Asymptote: compare
coefficients
-if top and bottom x^ values are equal,
then the top divided by the bottom is
the asymptote
- if the top x^ value is greater than the
bottom, there is NO asymptote
- if top x^ value is less than the bottom,
the asymptote is 0
Chapter Three
A. Exponential Growth vs. Decay
 USE CALCULATOR
B. Evaluating logarithmic functions without a
calculator
 logxY is really asking…
x elevated to what power will give
me y
 natural logs come in base 10 pairs
C. Rewriting Logarithms as Exponents

Log3x=5  35=x