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1. Dear math helper,

I am having problems with this question

I dont understand how to approach this question.
for example; is this how I draw the sketch of the periodic of f(x) = 2x
Attachment 572966572968

Attached Images

2. You've got the right idea with the sketch; but note that it starts at x=0 and looks like y=2x until you hit x=2. (So are you sure it goes negative?)

Try drawing a sketch on graph paper and label the graph a bit more; where does it go through zero? What is its maximum value before it goes back down again?

Then to answer the three parts it will be helpful to accurately draw y=2, and y=4-x/4. You should be able to see the pattern emerging as the line y=2 crosses your graph (a) to find a general solution, and by drawing y=4-x/4 you'll be able to see how many solutions there are (b).

Finally, for (c), you need to find the exact x-values where y=4-x/4 crosses the periodic function. The first part of the periodic function looks like the line y=2x, but stops at x=2. What line does the part that then starts from x=2 look like? (Hint: Its gradient is 2, but what is its y-intercept?) By finding the exact equation of the function within each interval where it crosses y=4-x/4 you will be able to solve for x explicitly.

Hope I helped!
3. (Original post by square_peg)
You've got the right idea with the sketch; but note that it starts at x=0 and looks like y=2x until you hit x=2. (So are you sure it goes negative?)

Try drawing a sketch on graph paper and label the graph a bit more; where does it go through zero? What is its maximum value before it goes back down again?

Then to answer the three parts it will be helpful to accurately draw y=2, and y=4-x/4. You should be able to see the pattern emerging as the line y=2 crosses your graph (a) to find a general solution, and by drawing y=4-x/4 you'll be able to see how many solutions there are (b).

Finally, for (c), you need to find the exact x-values where y=4-x/4 crosses the periodic function. The first part of the periodic function looks like the line y=2x, but stops at x=2. What line does the part that then starts from x=2 look like? (Hint: Its gradient is 2, but what is its y-intercept?) By finding the exact equation of the function within each interval where it crosses y=4-x/4 you will be able to solve for x explicitly.

Hope I helped!
I have sketch a new graph using desmos
I have uploaded my my revised answers but I still think that the number of general solution for part a and part b is 1
also the answer to part c is 16/9 if I am correct

Please like me know if I am heading in the right direction
Attached Images

Attached Images
4. Scanned from a Xerox Multifunction Device (5).pdf (23.9 KB, 5 views)
5. Scanned from a Xerox Multifunction Device (3).pdf (22.1 KB, 5 views)
6. Scanned from a Xerox Multifunction Device (4).pdf (22.7 KB, 7 views)

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