TEST TOMORROW..... can someone please help me?

katzmuzik26

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Apr 15, 2012
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We were given a practice test... and it's about functions, absolute value, and all that jazz.
I'm really stuck on a couple of problems. Correct me please if I'm wrong. anything in red i don't get...... at all.

4. How are the graphs of y=x^2 and y= (the absolute value of ) x similar? How are they different?
Ok, so I know that the absolute value of ANYTHING is the positive integer of itself, and I know that anything squared is the number times itself. They are alike because (i think) the end result will always be positive. They are different, because one does not require multiplication ???????????
6. A relation has the domain -1< x< 4 and a range of -4<y<5, and the x-value of 2 corresponds to the y-value 0.
a. Draw the graph of a function that fits this description
b. Draw the graph of a relation that fits this description but is not a function.
What the heck?! We did not go over this in class. HELP!
By the way, the < aren't necessarily <, they're supposed to have a line under them, to signify 'greater than or equal to'
8. The equation p(t)=600(1-0.087)^t describes a bacteria population where t represents time in hours.
b. how does the population change from one hour to the next?
d. Graph the equation & give the window you use. Is this relationship a function? Why or why not?
e. use your graph and the trace feature to find out how long it takes for the bacteria population to decrease to half it's original size.
Ok, I know B, I think. It decreases by 8.7% every hour. If you were to put it on your calculator, wouldn't it be y=600(1-.087)^x????


Longest post ever. Thanks for being patient with me and reading it! And thanks for any help you can give me!!!!!!!!!!!!
 
Hi,

well just in case no one else replies, here is what I think ( I am a little rusty on this stuff thought!)

We were given a practice test... and it's about functions, absolute value, and all that jazz.
I'm really stuck on a couple of problems. Correct me please if I'm wrong. anything in red i don't get...... at all.

4. How are the graphs of y=x^2 and y= (the absolute value of ) x similar? How are they different?
they are different because
-y=x^2 is not a linear function, while y=x is
- the domain of y= abosolute value of x is positive while with y=x^2 is can also be negative

they are similar because
- they are both functions
- they both go through the origin
- the domain of y is positive for both functions


6. A relation has the domain -1< x< 4 and a range of -4<y<5, and the x-value of 2 corresponds to the y-value 0.
a. Draw the graph of a function that fits this description

for this one draw they are telling you that the "allowable" x values are in between -1 and 4, so plot those points on a graph
(-1,0) and (4,0)

then, they are telling you that the allowable y values are -4 to 5, plot those (0,-4) and (0,5)

they also tell you that the x intercept is at 2

so now draw a line that will connect those points, I think it will be in the form of a cubic but make sure that it is clear that it does not continue beyond the desired points!

a quick test to see if something is a function is to draw a line through the graph, if for each value of x there is more than one associated y value, it is not a function, so draw a similar graph to the first one but make it so that it has this property. ( check here for an example http://www.purplemath.com/modules/fcns.htm)



8. The equation p(t)=600(1-0.087)^t describes a bacteria population where t represents time in hours.
b. how does the population change from one hour to the next?

sub in values of t in to the equation
p(t)=600(1-0.087)^t, what is happening, is it getting larger or smaller?

d. Graph the equation & give the window you use. Is this relationship a function? Why or why not?

see the above criteria

e. use your graph and the trace feature to find out how long it takes for the bacteria population to decrease to half it's original size.
If you were to put it on your calculator, wouldn't it be y=600(1-.087)^x????


hope that helps!
 
Ok Ok first step is to breath.

rbcc has the gist of it I will just add a few things.

4. \(\displaystyle y_1=x^2\) and \(\displaystyle y=|x|\) are similar because they have the same domain and range, and they are both even functions. They are different because generally \(\displaystyle y_1 \neq y_2\) and yes one is a polynomial the other is linear.

6. The information given is that x must be between -1 and 4, and the output or y values must be between -4 and 5. They also give you the x intercept at \(\displaystyle x=2\).

(a) A graph describing this will could be any graph that passes the vertical line test and spans these parameters. A starting point should be by placing a solid circle at (-1,-4) and a solid circle at (4,5) and a solid circle at the point (2,0). Connect these points making sure you always are moving in the x direction. Meaning you must always have a change in x. This will satisfy this graph being a function.

(b) Now for this to be not a function this graph must fail the vertical line test. Connect your three dots but spiral around a bit. Notice that for each input value you will have more than one output value. Hence failing the vertical line test.

8. (b) Yes each hour it is decreasing by 8.7% Good job.

(d) This sometimes takes trial and error. This is a function because it passes the vertical line test. Meaning for every t value you input you will get an unique population value as output.

(e) 600 is It's original size. So half of this is 300. You want to solve \(\displaystyle 300=600(.913)^t\). If you have not learned about logs you can graph this. Or as the problem suggests using the trace feature to see when the population value is 300.
 
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