Final answer:
The exponential function f(x)=3(0.75)^x has a horizontal asymptote at y=0 and a y-intercept at the point (0, 3).
Step-by-step explanation:
The exponential function in question is f(x)=3(0.75)^x. To find the asymptote of an exponential function, we look at the behavior of the function as x approaches positive or negative infinity. In this case, as x approaches positive infinity, the function approaches 0 since 0.75 raised to an infinitely large exponent will approach 0. As x approaches negative infinity, the term (0.75)^x becomes very large, but the function value is dominated by the coefficient 3 which remains constant. Therefore, the horizontal asymptote of this function is y=0.
To find the y-intercept, we set x to 0 in the function and solve for f(x). So, f(0) = 3(0.75)^0 = 3(1) = 3. Thus, the y-intercept of the function is at the point (0, 3).