math exam 1 Flashcards
1
Q
rational function equation
A
f(x) = [n(x)]/[d(x)]
2
Q
3 cases of HA
A
- n > d : slant
- n = d : leading coefficients ratio
- n < d : y=0!
3
Q
multiplicity
A
behavior of VA–
even: same direction, odd: opposite direction
behavior @ x-intercepts–
even: bounce, odd: cross
4
Q
to find a hole
A
- factor n & d, simplify
- crossed out terms: the hole
- plug in that x to find y, coordinate!
5
Q
to solve rational inequalities
A
- rearrange equation so simplified & equals 0
- finds the VAs (d) & the x-intercepts (n)
- make a number line with above values
- test intervals –> +? - ?
- write solution in interval form
6
Q
linear inequalities
A
if ONE variable: set builder notation
if TWO variables: graph solution
7
Q
vertex equation (for quadratics)
A
x = (- b)/2a
8
Q
to graph quadratic inequalities
A
- find the vertex
- factor: find holes, intercepts (have at least THREE points!)
- connect the dots & label function
- test & shade the solution: (0,0) is the easiest test
9
Q
to solve polynomial inequalities
A
- find x-intercepts & multiplicity
- make # line & test intervals
- interpret solution in interval notation (don’t include numbers that make d=0!)
10
Q
to determine domain of a function
A
- start w/ all real numbers
- if there’s a denominator, exclude values that make it 0
- if there’s a radical of even index, don’t include values that make it negative
11
Q
symmetry
A
even: f(-x)=f(x) –> across y-axis
odd: f(-x)= - f(x) –> across origin
neither: if f(-x) equals neither of above
12
Q
to find an inverse
A
- swap x & y
- solve for “y”
- make y “f ^-1 (x)”!
13
Q
to restrict domain
A
- break function @ vertex
- find each equation’s inverse
- revise inverse equation so applies to only that side
14
Q
inverse info.
A
- always reflected over y=x from og function
- will pass the horizontal line test
15
Q
transformations equation
A
y = af (bx + h) + k
a: vertical, stretch if >1
b: horizontal, stretch if 1>x>0
h: right if negative
