Question

What is the range of f(x)= (1/2)^x+3.

A) y>3
B) y<3
C) y is greater than or equal to 3
D) y> -3

Answer 1

Think about what happens to f(x) as you put in different numbers for x.
When x is negative, what does 1/2 raised to a negative exponent look like?

When x is 0, what is (1/2)^0 + 3?

What about when x is a positive number? For example, when x = 3 or x = 5?

Answer 2

Will (1/2)^x + 3 ever be a negative number or 0? What value does it approach as x becomes a very large positive number ?

Answer 3

@What is the range of f(x)= (1/2)^x+3 ?" is equivalent to asking, "what set of values include all of the possible outcomes of the function f(x) = (1/2)x + 3?

Have you tried graphing this function? It should be pretty obvious from the graph what the smallest y value is and what the largest is. @anteater's responses are very appropriate, and I'd suggest you answer both his/her questions if at all possible..

Answer 4

It's a "her" anteater. :)

Answer 5

For some reason we managed as a family to accumulate an inordinate number of Beanie Baby anteaters from McDonald's, back when they were putting Beanie Babies in the Happy Meals. They have been stacked around the computer, and so this is where the anteaters hang out. :)

Answer 6

If you graph f(x) = (1/2)^x + 3, you will see that it decreases (goes downhill) as you move from left to right. You may see exponential functions like this one referred to as "exponential decay" functions. (Exponential functions that increase are sometimes called exponential growth functions.) As mathmale said, if you were to plot some points and graph this curve you would notice that as x becomes larger y gets closer and closer to 3. It never quite reaches 3, though, but is always above 3. So, you would say that the line y = 3 is a horizontal asymptote of your graph.

Answer 7

I hope this was helpful! :)