Expert: Paul Klarreich - 11/16/2008

Question
Hello,

Can you please help me with this question?
It has two parts:

a.  Create an absolute value function that is true for
   each of the following:

1.  Vertex is in the 2nd quadrant
2.  Opens downward
3.  Opens wider than a standard graph of
   y=absolute value of x

List your function:

b.  Find all intercepts for this function.
   Show all your work.


Answer
Questioner:   Debbi
Category:  Advanced Math
Private:  No
 
Subject:  Algebra
Question:  Hello,

Can you please help me with this question?
It has two parts:

a.  Create an absolute value function that is true for
  each of the following:

1.  Vertex is in the 2nd quadrant
2.  Opens downward
3.  Opens wider than a standard graph of
  y=absolute value of x

List your function:

b.  Find all intercepts for this function.
  Show all your work.
..........................................
Hi, Debbi,

Try this approach:

Draw your 'basic function' for this type of example:  y = | x |

Now apply variations:

1. If you know what y = f(x) looks like, then

    y = f(x - a) moves to the right by 'a'.
    y = f(x + a) moves to the left by 'a'.

    y = f(x) + b  moves up by 'b'.
    y = f(x) - b  moves down by 'b'.

2. If you know what y = f(x) looks like, then

    y = - f(x) is upside-down.

3. If you know what y = f(x) looks like, then

    y = a f(x) is narrower (assuming  a > 1)

    y = b f(x) is wider (assuming  b < 1)

OK, take it from there.

As to intercepts, apply the rules your teacher told you:

Want  x-intercepts?  Set  y = 0 and solve.

Want  y-intercepts?  Set  x = 0 and solve.

If you do some work and get stuck, send me the work and I'll try to help.