SOLUTION: For x > 0, which of these statements best describe the graph of y = x^0.25 The slope is greater than zero and is decreasing. The slope is greater than zero and is increasing. Th

Question 1034609: For x > 0, which of these statements best describe the graph of y = x^0.25
The slope is greater than zero and is decreasing.
The slope is greater than zero and is increasing.
The slope is less than zero and is decreasing.
The slope is less than zero and is increasing.
None of the above
Answer by Theo(13342) (Show Source): You can put this solution on YOUR website!
you might want to look at a few points to see what's happening.

the equation is y = x^.25.

this is the same as y = fourth root of x.

this can also be written as y = x^(1/4).

let's look at x = 1,2,3,4.

when x = 1, y = 1
when x = 2, y = 1.1892071
when x = 3, y = 1.316074
when x = 4, y = 1.4142136

the slope between x = 1 and x = 2 is equal to (1.1892071) / 1 = .1892071.

the slope between x = 2 and x = 3 is equal to (1.316074 - 1.1892071) / 1 = .13268669.

the slope between x = 3 and x = 4 is equal to (1.4142136 - 1.316074) / 1 = .0981396.

looks like the slope is greater than zero and it is decreasing.

the graph of y = x^.25 is shown below:

you can see that the curve of the line rises less quickly as the value of x increases.

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