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Unit 3 , - Coggle Diagram
Unit 3
1.6
Higher-order polynomial equations
set the left had side of the equation to zero
Equations involving radicals
move one radical to the other side of the equation
square root both sides if possible
Factor by grouping
Arrange all terms in descending order
factor if possible
disguised quadratics
au^2+bu+c=0
solving a quadratic equation using substitution
1.7
Methods to describing a solution to an inequality
Gephing on a number line
writing it in set builder notation
writing it in interval notation
Linear equation
ax+b is less than c
a can't equal zeo
Inequalities involving fractions to decimals
find the LCD
cancel the fraction with a decimal
Three-part inequality
if you divide by a negative then the singe changes
compound inequality
if a solution involves and the both solutions are the answer to the inequality
if a solution end in or then only one answer is a solution to the inequality
1.8
Absolute value
standard form-IuI=c
properties of equations and inequalities
IuI=c - the the equation is u=c or u=-c
if IuI is less than c the the equation is -c is less than u which is less than c
if IuI is greater than c then the equation is going to be, u is less than -c or u is greater than c
Absolute value less than inequality
write n standard form
rewrite as a three part inequality
simpliyfy
1.9
polynomial inequality
solutions are called boundary points
Plotting these points for intervals
make sure to plug the answer back into the equation to check if its a solution
steps for polynomial inequality
make one side zero
factor
find all boundary points
plot points on a Number line
pick test value from each interval
substitute value into the expression
find the intervals that satisfy the equation
3.5
Sum of f and g
(f+g)(x)-f(x)+g(x)
Difference of f and g
(f-g)(x)=f(x)-g(x)
Product of f and g
(fg)(x)=f(x)g(x)
Quotient of f and g
(f/g)(x)=(f(x)/g(x))
g(x) can't equal 0
The domain of f of g
find the domain of g first
don't include in the domain of g all the x's that are not the domain of f
3.6
One to one function
if any value a does not equal b
f(a) does not equal f(b)
Alternate
for any two range values f(u) and f(v), f(u)=f(v) shows that u=v
Horizontal line test
for every horizontal line the graph intersect each line a most once
Interval function
f(a)=b, then f^-1=a
Finding the inverse function
change f(x) to y
interchange y and x
solve for y
replace y with f^-1(x)