Expert: Paul Klarreich - 3/7/2008

Question
I have quite a few questions but i need them tonight i could really use your help i am struggling during this unit!!


1.determine whether each graph is symmetric with respect to the x-axis, the y-axis, the line y=x, the line y=-x, the origin, or none of these.

a.x^2 y^2=9

b.5x^2 6x-9=y

2.Use the graph of the parent graph F(x)=x^2 to describe the changes between each function. Use complete sentences.
a.g(x)=(x-6)^2


b.h(x)=4(x 1)^2-8

3.Find the inverse algebraically. f(x)=(x-3)^2 7


Answer
Questioner:   David Vacha
Category:  Advanced Math
Private:  No
 
Subject:  Symmetry And Coordinate Graphs
Question:  I have quite a few questions but i need them tonight i could really use your help i am struggling during this unit!!


1.determine whether each graph is symmetric with respect to the x-axis, the y-axis, the line y=x, the line y=-x, the origin, or none of these.

a.x^2 y^2=9

b.5x^2 6x-9=y

2.Use the graph of the parent graph F(x)=x^2 to describe the changes between each function. Use complete sentences.

a.g(x)=(x-6)^2


b.h(x)=4(x 1)^2-8

3.Find the inverse algebraically. f(x)=(x-3)^2 7

...........................................
Hi, David,

Here's what you do for:

Symmetry:

1. Replace x by (-x) [USE PARENTHESES].  Does it come out the same?  L-R or y-axis symmetry.

2. Replace y by (-y) [USE PARENTHESES].  Does it come out the same?  U-D or x-axis symmetry.

3. Do both.  Does it come out the same?  Origin symmetry.

4. Swap the letters  x and y.  Does it come out the same?  Symmetry w.r.t  y=x

5. [this one is not common and I am not totally sure of it.]
Swap the letters  x and y AND replace both x,y with (-x,-y).  Does it come out the same?  Symmetry w.r.t  y=-x


2.Use the graph of the parent graph F(x)=x^2 to describe the changes between each function.
>> this is translation, stretching, etc.

Use complete sentences.

>> Oh, please! You do that anyway, don't you?


a.g(x)=(x-6)^2

Replace  x by  (x-a). [USE PARENTHESES]  Moves the graph 'a' units to the right.

In this case, it moves the graph 6 units to the right.

b.h(x)=4(x 1)^2-8

???????.  did you mean  (x+1)?

Changes:

x^2 -->  (x + 1)^2.  Moves 1 unit to the left.

(x + 1)^2 --> 4(x + 1)^2.  Stretches vertically by a factor of 4.

4(x + 1)^2 --> 4(x + 1)^2  - 8.  Moves 8 units DOWN.

.....................................

3.Find the inverse algebraically. f(x)=(x-3)^2 7

Are you having trouble with the '+' sign?  [I know the interface on this site might do that.  I will assume you meant:

f(x)=(x-3)^2 + 7

OOps -- I think we are in trouble here, as you will see.

Step 1:  Put y in place of f(x):

f(x) = (x-3)^2 + 7
  y = (x-3)^2 + 7

Step 2: Swap the letters x and y:

  y = (x-3)^2 + 7
  x = (y-3)^2 + 7

Step 3. Solve algebraically for y:

  x - 7 = (y-3)^2

y - 3 = +- sqrt(x - 7)  << That's the oops. Can't have +- here; you get two functions, not one and that is a no-no.

y = 3 +- sqrt(x - 7)

Step 4: Put f-inv(x) in place of y:

f-inv(x) = 3 +- sqrt(x - 7)

Well, we tried.