Transformations and Symmetry

Question 1

to shift a given graph up k units, f(x) = x becomes…

Answer 1

f(x) = x +k

Question 2

to shift a given graph k units right, f(x) = x becomes

Answer 2

f(x)=(x-k)

Question 3

to shift a given graph k units left, f(x) = x becomes

Answer 3

f(x)=(x+k)

Question 4

to reflect a graph about the y axis, replace x with…

Answer 4

-x

Question 5

what does f(-x) do to a graph f(x)?

Answer 5

reflect it about the y axis

Question 6

To reflect a graph in the x-axis, replace y by…

Answer 6

-y

Question 7

what does -f(x) do to graph f(x)?

Answer 7

shift about the y axis

Question 8

where do you put the negative in f(x) if it has been changed to -f(x)?

Answer 8

in the front of the entire function.
e.g f(x)=x-3
-f(x)=-(x-3)
=-x+3

Question 9

what does -f(-x) do to graph f(x)?

Answer 9

shift the graph 180 deg. aka flip the x axis and then the y axis, or vice versa

Question 10

A relation or a function is called even if its graph has line symmetry in the…

Answer 10

y axis

Question 11

algebriacally, how would you describe function f(x) if it was even?

Answer 11

f(x) = f(x-)

Question 12

A relation or function is called odd if its graph has…

Answer 12

point symmetry in the origin.
This means that the graph is unchanged by a rotation of 180°

Question 13

algebriacally, how would you describe function f(x) if it was odd?

Answer 13

f(x) = -f(-x)
OR
f(-x) = -f(x)

Question 14

When simplifying a composite function like
𝑔(f(x)), do the restrictions on the inner function
𝑓(x) still matter?

Answer 14

Yes, the restrictions on
f(x) still apply. You can only use
x-values that are allowed by f(x).