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What is the y intercept, function, domain and range, and horizontal asymptote of y=0.25^x ?

User MerlinND
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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.

User Msmazh
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