Question

Consider the function f left parenthesis x right parenthesis equals 1.3 left parenthesis 1.85 right parenthesis to the power of x. what is the y-intercept [a], asymptote [b], domain [c], and range [d]? is this a growth or decay function [e]?

Answer 1

The function f(x) = 1.3(1.85)^x has a y-intercept of 1.3, no horizontal asymptote, a domain of all real numbers, a range of all positive real numbers, and represents exponential growth.

Step-by-step explanation:

Interpreting the Function

For the function f(x) = 1.3(1.85)^x, we can find the following characteristics
Y-intercept: To find the y-intercept, let x = 0. This gives us f(0) = 1.3(1.85)^0 = 1.3. Therefore, the y-intercept is 1.3.

Asymptote: Since this is an exponential function and does not approach a horizontal line as x tends towards plus or minus infinity, there is no horizontal asymptote. However, the x-axis (y=0) is a horizontal asymptote as x approaches negative infinity if you consider the graph from a practical perspective, where the function values become insignificantly small.Domain: The domain of any exponential function is all real numbers, so here it is (-∞, ∞).Range: The range of this function is all positive real numbers, so (0, ∞).

Growth or Decay: Since the base of the exponent, 1.85, is greater than 1, this function represents exponential growth.