SOLUTION: A graph has the following key features:
Decreasing for x > 0
y-intercept of 1
No x-intercept
A horizontal asymptote of y = 0
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Question 191149: A graph has the following key features:
Decreasing for x > 0
y-intercept of 1
No x-intercept
A horizontal asymptote of y = 0
Domain: {x|xER}
Range:{y|y > 0, yER}
(1, 0.5) is a point of the graph
A possible function with all these key features is ______________________.
Answer by solver91311(24713) (Show Source): You can put this solution on YOUR website!
A function that is decreasing on x > 0, y-intercept of 1, no x-intercept, and asymptotic to the x-axis (i.e. y = 0),
domain 
, range 
is:
 = a^{-x})
where 
is any real number > 0, in other words a reflection of the general exponential function about the y-axis.
But you are looking for such that 
and that number would be 2.
 = 2^{-x})
The only thing that bothers me about this is the statement that f(x) is decreasing on the interval x > 0. In fact, the function is decreasing across its entire domain. That doesn't make this wrong, because the parameters of the problem don't specify what the function has to be doing on x <= 0. But it makes me wonder what the question writer was thinking. For that matter, why did the writer specify no x-intercepts when the range is restricted to values greater than zero?
John
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