Question

Identify whether each of the following are polynomial functions or exponential functions. For polynomial functions identify the degree of the function, and for exponential functions identify the base. a) y=−3(16)x+19 b) y=2x6+3x3−17x+9 c) y=2(52​)x−15 d) y=x2−7 e) y=6(4)x−5

Answer 1

Equations a), c), and e) are exponential functions with bases 16, 5/2, and 4 respectively. Equations b) and d) are polynomial functions with degrees 6 and 2 respectively.

Step-by-step explanation:

To determine whether each function is a polynomial or an exponential function, we will analyze the form of each equation.

• a) y = -3(16)^x + 19: This is an exponential function. Its base is 16.
• b) y = 2x^6 + 3x^3 - 17x + 9: This is a polynomial function. The highest exponent is 6, so its degree is 6.
• c) y = 2(5/2)^x - 15: This is an exponential function with a base of 5/2.
• d) y = x^2 - 7: This is a polynomial function. It is a quadratic polynomial (degree 2) because the highest exponent is 2.
• e) y = 6(4)^x - 5: This is an exponential function. Its base is 4.

The degree of a polynomial is the highest exponent the variable has in the function. Exponential functions, in contrast, have the variable as an exponent on a constant base.

Learn more about Polynomial vs Exponential Functions