Functions Q: Use your graph to estimate...

[MuddledMaths]

Hey I'm having troubles with this question hope you guys can help? It's about functions
Ignore the writing btw, only the top one is right :/
The answers didn't make much sense to me.

 

[Dr.Peterson]

Hey I'm having troubles with this question hope you guys can help? It's about functions
Ignore the writing btw, only the top one is right :/
The answers didn't make much sense to me.

Please tell us something of your own thoughts. What about the answers doesn't make sense? How did you try to answer the questions?

The graphs you drew are basically right, and the rest is about reading the graphs.

 

[MuddledMaths]

Well i didn't get (ii) when it says the third value of X, I tried to match the answer at the back after realising six was wrong but I couldn't do it. Like I put in the two functions and tried to find a common number (0.77) but they didn't match on my calculator. I'm probably doing this wrong but the values aren't matching

 

[MuddledMaths]

And the range of values one completely confused me. What does the straight line with the X mean in a set?

 

[blamocur]

And the range of values one completely confused me. What does the straight line with the X mean in a set?

What are you studying? Doesn't your textbook and/or lecture notes have definitions for ranges and the notations in the answers?

 

[Dr.Peterson]

Well i didn't get (ii) when it says the third value of X, I tried to match the answer at the back after realising six was wrong but I couldn't do it. Like I put in the two functions and tried to find a common number (0.77) but they didn't match on my calculator. I'm probably doing this wrong but the values aren't matching

They say to use your graph to estimate. If they mean to use the graph you drew, then it would be something like this:

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You circled the right point; I show my answer for the third point as being around -0.8. I wouldn't expect to estimate any closer than that. Their answer of -0.77 is probably obtained from a graph on a graphing calculator or the like:

​

And the range of values one completely confused me. What does the straight line with the X mean in a set?

I guess you are referring to this:

​

They are using set-builder notation; they could instead have used interval notation. Have you not been taught about the former?

The first part of their answer is read as "the set of all x such that x is between -0.77 and 2".

 

[MuddledMaths]

These are exam papers and I'm studying for a junior cert so the textbook doesn't give the same kind of questions.
So do you think I'd still get the marks if I estimated 0.8 or 0.7 because I thought there would be some formula to get the 0.77 like when you get the table of values

 

[MuddledMaths]

I don't get the terms you used there for the notation because I honestly haven't heard them till now but the sentence in words at the bottom makes more sense. Would it be okay if I wrote
X is 2^x > x² in the range {0.8<X<2} and {X>4}, X is an element of R

 

[MuddledMaths]

We use interval notation but we never called it that

 

[blamocur]

These are exam papers and I'm studying for a junior cert so the textbook doesn't give the same kind of questions.
So do you think I'd still get the marks if I estimated 0.8 or 0.7 because I thought there would be some formula to get the 0.77 like when you get the table of values

Watch your signs

 

[MuddledMaths]

Whoops oh ya

 

[Dr.Peterson]

These are exam papers and I'm studying for a junior cert so the textbook doesn't give the same kind of questions.
So do you think I'd still get the marks if I estimated 0.8 or 0.7 because I thought there would be some formula to get the 0.77 like when you get the table of values

Since the problem says to "use your graphs to answer ... estimate a third value", clearly they don't want you to use a formula.

You could make a table of values as you did, and when you find the answer is between -0.8 and -0.7, then make a table by hundredths over just that interval; but they didn't say they wanted the nearest hundredth, so why bother?

Don't expect more of yourself than the problem states. Read carefully.

I don't get the terms you used there for the notation because I honestly haven't heard them till now but the sentence in words at the bottom makes more sense. Would it be okay if I wrote
X is 2^x > x² in the range {0.8<X<2} and {X>4}, X is an element of R

They didn't say what form the answer should take, so just writing in words something like "x can be between about -0.8 and 2, or greater than 4" would probably be fine. What you wrote might be better.

But if this is a sample problem from the maker of the exam, and they imply, as they do, that they expect you to know set-builder notation, then you may want to study it ...

 

[blamocur]

They say to use your graph to estimate. If they mean to use the graph you drew, then it would be something like this:

View attachment 35936​

You circled the right point; I show my answer for the third point as being around -0.8. I wouldn't expect to estimate any closer than that. Their answer of -0.77 is probably obtained from a graph on a graphing calculator or the like:

View attachment 35937​

I guess you are referring to this:

View attachment 35938​

They are using set-builder notation; they could instead have used interval notation. Have you not been taught about the former?

The first part of their answer is read as "the set of all x such that x is between -0.77 and 2".

Somehow I find it amusing that the solution is close (within 2e-6) to -23/30

 

[MuddledMaths]

Okay thank you so much for your help, my exam is on Friday and I'm going full painic mode and one of my least favourite chapters is functions but I understand it better now. Thank you!