Question

What is the range of the following function?


Select one:
a. All irrational numbers
b. All real numbers
c. All negative numbers
d. All positive numbers

Answer 1

@zepdrix

Answer 2

@phi

Answer 3

Let's just test a point and see what happens.
Plugging in \(\Large\rm x=0\),
what do you get for y?\[\Large\rm y=3\left(\frac{1}{2}\right)^0\]\[\Large\rm y=?\]

Answer 4

would it be 1.5 or 9

Answer 5

or i mean 6

Answer 6

Recall that when we raise to the 0 power, we end up with 1.

Answer 7

oh yes so 3

Answer 8

Ok good.
So the value 3 is in our range.

Let's examine what type of number 3 is.

Answer 9

Is 3 `irrational`?

Answer 10

no

Answer 11

its either b or d right

Answer 12

3 is `rational`, ok good.
3 is also not `negative`.
`Negative`, `positive`, and `irrational` are all included in the reals.

Ooo this is bad logic that I'm setting up though.

I was trying to say that since 3 is none of the first 3,
then it must be the positives.

But that doesn't tell us that it can't be negative.

Ok ok lemme try to be a little bit more clear >.<

Answer 13

Here is what an exponential function looks like.
See how the curve is ALWAYS above the x-axis?