Graphing Techniques

Question 1

What dilation is a reflection

Answer 1

A scale factor of -1

Question 2

If the dilation factor is between 0 and 1…

Answer 2

graph is compressed

Question 3

How to apply an enlargement with a factor a

Answer 3

Replace x by x/a and y by y/a

y = af(x/a

Question 4

How to dilate graph in the horizontal direction by a factor a

Answer 4

replace x by x/a

Question 5

How to dilate graph in the vertical direction by a factor of a

Answer 5

replace y by y/a

y=af(x)

Question 6

How to rotate 180 degrees about the origin

Answer 6

Replace x by -x, y by -y

y=-f(-x)

Question 7

How to reflect in the x-axis

Answer 7

Replace y by -y

y=-f(x)

Question 8

How to reflect in y-axis

Answer 8

Replace x by -x

Question 9

How to solve a quadratic inequation

Answer 9

Move everything to LHS
Sketch y=LHS
Read solution off graph

Question 10

How to solve absolute value inequations

Answer 10

Take both + and -

Question 11

How to shift graph horizontally left

Answer 11

replace x by x+h

Question 12

How to shift graph horizontally right

Answer 12

replace x by x-h

Question 13

How to shift graph vertically

Answer 13

Replace y by y-k (up) or y+k (down)

Question 14

What is an enlargement factor of -1

Answer 14

rotation 180 about the origin

Question 15

How to test for vertical asymptotes

Answer 15

Factor first

Let denom = 0 then solve, test solutions in numerator

Question 16

How to test for horizontal asymptotes

Answer 16

Divide top and bottom by highest power of x in the denominator
Then replace anything a/x with 0 and solve

Question 17

Dilations of y=kf(x) when k changes

Answer 17

k>1 graph stretched

0

Question 18

Dilations of y=f(ax) when a changes

Answer 18

a>1 graph compressed

0<a></a>

Question 19

effects of (a,h,k) on a hyperbola graph (y=a/x-h +k)

Answer 19

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

Question 20

horizontal dilation scale factor

Answer 20

given y=f(ax)

scale factor= 1/a

Question 21

How to sketch curves

Answer 21

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)

Question 22

How to solve linear equations

Answer 22

same method as linear equations but when x or divide by negative number, reverse the inequality sign

Question 23

Dilating in the vertical direction…

Answer 23

Changes all y values by a factor of a