For the function , make a table with integer values of x from 0 to 4. Then graph the function (you do not need to submit the graph). Does the graph of show exponential growth, exponential decay, or neither? Explain your thinking.

Question

anonymous · Answer

$$y =1^{x}$$

ddcamp · Answer

Fill in the graph and plot the points:
|dw:1368851559489:dw|

If you want, clicking the pen on the top corner of the drawing will allow you to draw over what's already there.

hunus · Answer

What are the values of y in these cases?$$y=1^0$$$$y=1^1$$$$y=1^2$$$$y=1^3$$$$y=1^4$$

anonymous · Answer

Im trying to understand what  integer values of x are.

e.mccormick · Answer

Integer, the numbers without decimals or fractions.

ddcamp · Answer

So you only test whole numbers (1,2,3,-1,-5,0, to name a few)

e.mccormick · Answer

Huh? -1 and -5 are not whole nunbers.

anonymous · Answer

but x = 1 isn't it ture that 1^x is always 1

hunus · Answer

Yes

e.mccormick · Answer

Yes GertheDL, they are all 1.  What does that look like? Exponential growth, exponential decay, or neither?

anonymous · Answer

so there is no growth or decay?

hunus · Answer

Does y ever equal anything besides 1?

anonymous · Answer

nope

e.mccormick · Answer

Yep GertheDL!  It is neither.

-7, 259, 42 and things like that are all integers.  Where as $\frac{1}{3}$ is a rational number (from ratio).  In contrast, $\pi$, $e$, and $\sqrt{2}$ are irrational as in they can not be represented by a ratio.  There are also complex, whole, counting, and a few others.  Real numbers is an important category. Whole numbers are the integers $\ge 0$.

hunus · Answer

So it doesn't grow or decay :)

e.mccormick · Answer

When you do the explain your thinking part, what you said about $1^x=1 \forall x \in \mathbb{Z} \ge 0$ will be good.