Final answer:
The properties of the function y=0.25^x are: the y-intercept is 1, the function represents an exponential decay, the domain is all real numbers, the range is greater than 0, and the horizontal asymptote is y=0.
Step-by-step explanation:
To determine the properties of the function y=0.25^x, we will analyze it step-by-step:
- Y-intercept: The y-intercept is the value of y when x is 0. So, for the given function, when x=0, we have y = 0.25^0 = 1. Hence, the y-intercept is 1.
- Function: The function y = 0.25^x represents an exponential decay because 0.25 is between 0 and 1.
- Domain: The domain of an exponential function is all real numbers, so the domain of this function is (-∞, ∞).
- Range: The range of an exponential decay function is greater than 0, so the range of this function is (0, ∞).
- Horizontal Asymptote: As x tends to infinity, the function approaches zero, so the horizontal asymptote is y = 0.