Question

let y=(1/2)^x
find the y intercept write an ordered pair and find the range either set or interval notation

Answer 1

To find the y-intercept, set x = 0 and solve for y.

Answer 2

wouldn't y be 0 then also

Answer 3

No. (1/2)^0 = 1

Answer 4

oh because the x is ^

Answer 5

correct.

Answer 6

so (0,1) would be the ordered pair

Answer 7

and that is the y intercept?

Answer 8

yes. That would be the ordered pair for the y-intercept.

Answer 9

ok how do I find the Range then?

Answer 10

There is no restriction on x and therefore the domain for x is: (-infinity, infinity).
If I put x = -very large number then y = (1/2)^(-very large number)
1 / 2^(-very large number) = 2^(very large number)
When I bring the 2 to the numerator, the negative in the exponent goes away because
1/a^(-m) = a^m

2^(very large number) is a very large number and when the very large number is infinity then y will go to infinity too. positive infinity.

When x becomes very large, then y becomes (1/2)^very large number. So the denominator will become very large and y will go to 0.

So the range is (0, infinity)

Answer 11

and on a graph I would start with the (0,1) and draw through the 0?

Answer 12

or start at the (0,1) and draw up and towards the right on the graph?

Answer 13

It will look like this:

Answer 14

ok thank you!

Answer 15

you are welcome.