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nycguitarguy

Member

Registered: 2024-02-24

Posts: 546

Graph Involving Absolute Value

A graph has the following points joined by a straight line from A to D, in that order.

A = (-2, -1)

B = (-1, -1)

C = (1, 1)

D = (2, 0)

A. Draw the graph of y = | f(x) |.

B. Draw the graph of y = f(| x |).

C. What is the basic difference between the two graphs?

Bob

Administrator

Registered: 2010-06-20

Posts: 10,198

Re: Graph Involving Absolute Value

A = (-2, -1)

B = (-1, -1)

C = (1, 1)

D = (2, 0).

A. Draw the graph of y = | f(x) |.  You have to work out f(x) and then make any negative values into positives. Some are already positive and so those are unchanged.

B. Draw the graph of y = f(| x |) You have to change any negative x values into positives; then use the function to work out what y values you get.  I found that the original 4 points become just 2 points repeated.

What is the basic difference? Neither new graph looks anything like the original; nor do they share any similarities. Hard to see what the questioner is searching for here.

What you can say is that  y = | f(x) | has no negative y values and  y = f(| x |) has no negative x values.  Is that what is wanted?

Bob

---

Children are not defined by school ...........The Fonz
You cannot teach a man anything;  you can only help him find it within himself..........Galileo Galilei
Sometimes I deliberately make mistakes, just to test you!  …………….Bob

nycguitarguy

Member

Registered: 2024-02-24

Posts: 546

Re: Graph Involving Absolute Value

A = (-2, -1)

B = (-1, -1)

C = (1, 1)

D = (2, 0).

A. Draw the graph of y = | f(x) |.  You have to work out f(x) and then make any negative values into positives. Some are already positive and so those are unchanged.

B. Draw the graph of y = f(| x |) You have to change any negative x values into positives; then use the function to work out what y values you get.  I found that the original 4 points become just 2 points repeated.

What is the basic difference? Neither new graph looks anything like the original; nor do they share any similarities. Hard to see what the questioner is searching for here.

What you can say is that  y = | f(x) | has no negative y values and  y = f(| x |) has no negative x values.  Is that what is wanted?

Bob

Yes, you are right. This is what Sullivan is asking for in his book.