Graphing Techniques Flashcards
(23 cards)
What dilation is a reflection
A scale factor of -1
If the dilation factor is between 0 and 1…
graph is compressed
How to apply an enlargement with a factor a
Replace x by x/a and y by y/a
y = af(x/a
How to dilate graph in the horizontal direction by a factor a
replace x by x/a
How to dilate graph in the vertical direction by a factor of a
replace y by y/a
y=af(x)
How to rotate 180 degrees about the origin
Replace x by -x, y by -y
y=-f(-x)
How to reflect in the x-axis
Replace y by -y
y=-f(x)
How to reflect in y-axis
Replace x by -x
How to solve a quadratic inequation
Move everything to LHS
Sketch y=LHS
Read solution off graph
How to solve absolute value inequations
Take both + and -
How to shift graph horizontally left
replace x by x+h
How to shift graph horizontally right
replace x by x-h
How to shift graph vertically
Replace y by y-k (up) or y+k (down)
What is an enlargement factor of -1
rotation 180 about the origin
How to test for vertical asymptotes
Factor first
Let denom = 0 then solve, test solutions in numerator
How to test for horizontal asymptotes
Divide top and bottom by highest power of x in the denominator
Then replace anything a/x with 0 and solve
Dilations of y=kf(x) when k changes
k>1 graph stretched
0
Dilations of y=f(ax) when a changes
a>1 graph compressed
0<a></a>
effects of (a,h,k) on a hyperbola graph (y=a/x-h +k)
a: vertical dilation by factor of a
if a<0 graph reflected in x-axis
h: horizontal translation of h
k: vert translation of k
horizontal dilation scale factor
given y=f(ax)
scale factor= 1/a
How to sketch curves
factor/combine fractions
find domain
even,odd or neither to find symmetry
x and y intercepts
table of signs
vert asymptotes (examine behavior around)
hori asymptotes (examine behavior around)
How to solve linear equations
same method as linear equations but when x or divide by negative number, reverse the inequality sign
Dilating in the vertical direction…
Changes all y values by a factor of a
