Question 398901: State whether the equations represent a linear, quadratic, or exponential function
1) y=2^x^2
I thought this would be exponential but not sure since the ^x is not a number and that is squared.
2)10x+7-y=0
At first I thought this was linear but to make it in linear format it would be 10x+7=y which is not y=mx+b so I now think this is not any of the options.
3)y=10^2^x
I feel this is exponential.
Am I correct? So confused.
Found 2 solutions by jsmallt9, lwsshak3:
Answer by jsmallt9(3758)   (Show Source):
You can put this solution on YOUR website! #1 and #3 are similar problems.
If the only choices are linear, quadratic and exponential, then they must both be exponential because they are definitely not linear or quadratic. With linear equations, the variables are not in exponents and the exponents on the variables are always 1's. With quadratic equations, the variables are not in exponents and the exponent on one variable is a 1 and the exponent on the other variable is a 2.
2)10x+7-y=0
At first I thought this was linear but to make it in linear format it would be 10x+7=y which is not y=mx+b...
It's not? It sure looks like y = mx+b to me! (Remember that you can flip the left and right sides of any equation. So 10x+7 = y is the same as y = 10x+7.)
In any event you don't have to write it in slope-intercept form (y = mx+b). All you have to see is that the variables are not in exponents and the variables have exponents that are 1's. This makes it a linear equation.
P.S. In your note you said that "none of the above" was also a choice. In that case I am not sure of the answer for #1 and #3. The reason I am not sure is that I am not sure what the expressions are. For #1 is it
or
 ?
These are not the same and the first one is not what I would call an exponential equation. The second one, as the other tutor has shown, is equivalent to  which I believe is exponential.
Similarly for #3. Is it
or
The first one is not exponential. The second one is equivalent to  which is clearly exponential.
If the expressions were given just as you wrote them (i.e. without any parentheses or any other indication as to what the outermost exponent applies), then I believe the first interpretations of each, which are not exponential, are correct.
In general exponents apply only to what is immediately in front of them. A simple example of this is -4^2. A lot of people think this means -4 squared (or 16). But the exponent only applies to the 4, not the mines! -4^2 means "the negative of 4 squared" (which is -16)
So in 2^x^2 the exponent of two applies just to the x and not to 2^x. In other words 2^x^2 means a product of x^2 2's multiplied together while (2^x)^2 means 2 2^x's multiplied together or 2^(2x). These are not the same thing. And the first is not what I would call exponential while the second one is.
Answer by lwsshak3(11628) (Show Source):
You can put this solution on YOUR website! 1) y=2^x^2=2^x*2^x
This is the same as y=2^2x. Remember the rule in algebra? Raising any number or variable to a power,results in a single term with its exponent= product of the individual exponents. With the variable in the exponent this is an exponential function
2)10x+7-y=0
Change it to standard form, y=10x+7, and you can see it is a straight line (linear function) with slope=10 and y-intercept at 7
3)y=10^2^x
This is the same as y=10^2x, Like 1),with the variable in the exponent this is an exponential function
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