Question

Which statements are true of the function f(x) = 3(2.5)x? Check all that apply.

Answer 1

Answer:

a) the function is exponential

c)the function increases by a factor of 2.5 for each unit increase in x

d)the domain of the function is all real numbers

Step-by-step explanation:

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Answer 2

This is an exponential function since the x is in the exponent's place instead of in the place of a "regular" variable. The first statement is true.

The initial value of this particular function is 3 (the other number is the multiplier), so choice 2 is NOT true.

The function increases by its multiplier, which is 2.5, so statement 3 is true.

The equation allows us to enter any x value we want to determine the y, so the domain is in fact all real numbers. So, this statement is also true.

If you were to graph this on a calculator, you would see that the range, the "allowed" y values for our function, do not touch or ever drop below the x-axis. That means that the range is all numbers greater than 0. So that statement is false. No matter what value we pick for x, we will NEVER get back a negative y value or that y = 0. For example, if x = 0, y = 3; if x = -5, y = .03; if x = -10, y = .0003; if x = 5, y = 292.97; if x = -100, $y = 4.8208*88888810^{-40}$. Y will never be equal to 0 or less than 0.