College Algebra Chapter 4 notes:
Slope of a Vertical line undefined
Slope of a Horizontal line 0
Equation of a line- point slope form yy=m(xx)
Equation of a line-slope intercept form y=mx+b
b=y intercept
Equation of a line-horizontal line y=k
Equation of
College Algebra chapter 7 notes:
Stretch & Compress g(x)=af(x) a>0 has the same shape as f(x); taller if a>1 and flatter if 0<a<1
Stretch & Compress-away from y g(x)=f(bx) stretch away from y-axis if 0<b<1 and compressing toward y-axis if b>
1
Sums of Fun
College Algebra chapter 9 notes:
Commutative Property of Addition - a + b = b + a
Counterexample - an example that proves a statement false
Data - information; facts, figures, statistics used to describe something
Distributive Property a(b+c)=ab+ac
Domain
College Algebra chapter 6 notes:
Cubing Function f(x)=x graph= through origin across y-axis
D (,) R (-,) odd function
Absolute Value Function f(x)=|x| graph= V
D (,) R [0,) even function
Square Root Function f(x)=(x) graph= extending (0,)
D (x0) R (0,)
Cu
College Algebra Chapter 5 notes:
Vertical Line Test - intersects at no more than one point=graph of a function
Domain of a Function - the largest set of real numbers for which f(x) is a real
number, if a function f is defined by an equation
Average Rate o
College Algebra Chapter 8 notes:
Horizontal Line Test - intersects in at most one point, then f(x) is a one-to-one function
Inverse Function - g=f(x) if function is 1:1
Graph of an Inverse Function - graph of f is reflection of graph f over the line y=x
T
College Algebra Chapter 3 notes:
Distance Formula d(P,Q)=[(xx)+(yy)]
P (x,y) Q (x,y)
Midpoint Formula M(x,y)=[(x+x)/2, (y+y)/2]
P(x,y) Q(x,y)
X-intercepts - where graph touches x-axis or crosses
set y=0 and solve for x
Y-intercepts - where graph touches y
College Algebra Chapter 10 notes:
Identity - an equation that is true for all values of the variable
Identity Property of Addition - the sum of any number and zero is the original number
Identity Property of Multiplication - the product of any number and
College Algebra Chapter 1 notes:
Quadratic equation - ax^2+bx+c=0 a not equal to 0
Zero Product Property - A*B=0 and A=0 or B=0
solve ax^2+bx+c completing the square - subtract c from both sides, divide both sides
by the leading coefficient a, Compare (1/
TO STUDY FURTHER:
Natural numbers
Integers
Rational numbers
Irrational numbers
Real numbers
Venn diagrams pictures of sets
rational number is a number that can be expressed as a quotient of 2
Decimals - TRUNCATE removes digits, ROUNDING rounds them
arithm