Inverse functions
When the x and y values are switched.
*functions only have inverses if they are one-to-one
Identity function
The function that maps every element of the domain to every element of the range
*simple def-the x value is the same as the y value
Composition of functions
When two or more functions are evaluated at the same time. The two function will always be given to you and all you need to do is determine which one to evaluate first.
Notations (there are two)
F(g(x)) means f of g of x, which means evaluate g(x) first and then evaluate that result using f(x)
Inverse variation
When two numbers are proportional. *written as a fraction Y=a/x a doesn't equal 0 Xy=a a is the constant of variation and y is said to vary inversely with x
Inverse variation ex.
Y varies inversely as x. If, y=6& x=-3, find y when x=4
Step 1: write inverse variation equation.
Step 2: substitute -3 for x & 6for y
Step 3:solve for a
Step 4: write an equation that relates x& y
Step 5:substitute 4 for x
Step 6: reduce
What is the general equation of a circle? (aka center-radius form)
(x-h)squared+(y-k)squared=r squared
R is the length of the radius and(h,k) is the center of the circle.
***note the h and k are opposite signs in the equation.
General form
X squared+ y squared+Dx+Ey+F=0
Where: D=-2h E=-2k F=h squared +k squared-r squared
Solving quadratic equations
Steps:
- Write in standard form and set equal to zero.
- Factor
- Set each parenthesis equal to zero and solve.
- Check each answer.
Solving quadratic inequalities
Steps:
- Get into standard form
- Factor
- plot number(s) on number line
- Test values in each section
Simplify rational expressions with factorable parts
Steps:
- Factor both numerator and denominator.
- Reduce any terms that are exactly the same to one.
- Reduce any terms that are opposite AND subtraction to (-1)
- Reduce any GCF coefficients.
