In Exercises 11-16 , determine whether the function is a...

In Exercises $11-16$ , determine whether the function is a monomial function, given that $l$ and $\pi$ represent constants. For those that are monomial functions state the degree and leading coefficient. For those that are not, explain why not.
$$
y=-2 \cdot 5^{x}
$$

Labs

Want to see this concept in action?

NEW

Explore this concept interactively to see how it behaves as you change inputs.

View Labs

Key Concepts

Monomial Function

A monomial function is a single-term function of the form a*x^k, where a is a constant (the coefficient) and k is a nonnegative integer (the degree). This structure is a subset of polynomial functions and allows for the clear definition of both the degree and the leading coefficient.

Exponential Function

An exponential function is one in which the variable appears in the exponent, typically written in the form a*b^x. Unlike monomial functions, exponential functions do not have a fixed degree and do not adhere to the polynomial structure because the exponent is not a constant but rather a function of x.

Degree

In the realm of polynomial functions, the degree is the highest power of the variable present, and in a monomial it is given explicitly by the exponent in the term a*x^k. This concept does not apply to exponential functions because the variable is in the exponent rather than multiplying a base variable raised to a fixed power.

Leading Coefficient

The leading coefficient in a monomial or polynomial function is the coefficient of the term with the highest degree. It influences the behavior of the function, particularly for large values of the variable. This notion is not applicable to exponential functions due to their differing structure from polynomial expressions.

Please give Ace some feedback