Math Is Fun Forum

I think so.

It would have been better if the questioner had said "For each function identify if it is decreasing, increasing or neither including where in the domain this occurs." But they possibly thought it was obvious.

Bob

Is this right? No. You're charging too much.

For part 2, 100 miles has already been charged so 0.4 only applies for 200 miles (300 minus 100)

Same for the remaining parts. Subtract the miles that have already been charged to determine how many more miles to charge at the next rate.

A step function graph looks like a staircase, flat parts getting higher.

This graph has sloping lines with gradients 0.5, 0.4, 0.25, 0 so the sections go up in sloping lines except for the last which is flat.

Bob

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

Part A fully correct.

Looks like a typo crept in for B . (3,12) was correct but then you put (3,10)

Bob

I've added an extra column to my table:

0 < x ≤ 100                      cost per mile 0.5  max cost = 100 x 0.5 = 50
100 < x ≤ 300                   cpm 0.4               max cost = 200 x 0.4 = 80
300 < x ≤ 400                    cpm 0.25              max cost = 100 x 0.25 = 25
400 < ≤ 960                       cpm no charge

This looks ok.

Not  x ≤ 400. The upper limit for part 2 is 300.

Where did 170 come from?

Bob

Mathematically, this is similar to the truck charge question.  First summarise the info.

0 < weight ≤ 1              fixed charge of 1.17
1 < x ≤ 13                    0.17 per ounce

So between x=0 and 1 the graph will be a horizontal line as the charge is fixed and doesn't vary with x.

After that the additional cost starts to go up in a straight line with gradient 0.17 .

The graph stops when x=13

Bob

That's it. Well done.

Bob

Yes to both.

Bob

No. You want x + 4 = -8

Part B is correct.

Bob

Oh I see what happened. I read post 2 not noticing post 1.

Part B correct not A. It's to do with where the 2 is . Inside the bracket, ok. Outside it doubles the y coordinate and does nothing to the x.

Bob

Again refer to the graph on a previous thread.

To get h(x) 2x inside the bracket is the same as squeezing the points closer to the y axis by a factor 1/2. The y coordinates stay the same.

eg (-4,-2) moves to (-2,-2)

g(x) reflects the points in the y axis so (-4,-2) becomes (+4,-2)

Comment on the number of posts.

I don't mind lots of posts if it means I'm helping you.  But it does get hard to keep track when so many appear at once.

Two suggestions that would help me:

Either (1) number your posts in the title so I can keep track of which ones I've viewed and dealt with,

Or (2) post the next query in the same thread you are already using so we get a chain of items all in one longer thread.  I did it that way some years back for an English lady who was studying for GCSE (late entrant). Her thread got to thousands of individual posts but it was easy for both of us to keep track.

Bob

They want you to say if the transformed graph has a decreasing or increasing section and if so where.

Bob