Question

Which of the following choices describes the function?

an exponential function that is decreasing.
a quadratic function that is increasing then decreasing.
a quadratic function that is decreasing then increasing.
None of these choices are correct.

Answer 1

Answer: The function that is an exponential function that is decreasing is described as:

an exponential function that is decreasing.

A quadratic function that is increasing then decreasing would have a U-shaped graph, and a quadratic function that is decreasing then increasing would have an inverted U-shaped graph. However, neither of these options describes an exponential function that is decreasing.

Therefore, the correct choice is: an exponential function that is decreasing.

Step-by-step explanation:

Answer 2

Neither a linear nor a quadratic function fits the description of a function with a positive, yet decreasing slope as x increases. Thus, none of the choices provided are correct for a function with these characteristics.

Step-by-step explanation:

The student's question is centered around determining the type of function that could be represented by the information provided. Given that at x = 3, the function f(x) has a positive value with a positive slope that is decreasing in magnitude with increasing x, none of the provided options explicitly match this description. However, if we analyze the descriptions carefully:

Option a, y = 13x, suggests a linear function, which has a constant slope and therefore does not fit the description.

Option b, y = x², is a quadratic function, which typically has a slope that changes in magnitude. For x>0, the slope of a quadratic function generally increases as x increases, which also does not correspond to the given function's characteristics.

Since neither linear nor quadratic functions match the description where the function has a positive slope that decreases, we conclude that None of these choices are correct.