Question

Use a determine if the function is a polynomial calculator.

a) f(x) = √(x^2 + 1)
b) g(x) = x^3 + 2x^2 - 4
c) h(x) = 1/x
d) k(x) = e^x

Answer 1

To determine if a function is a polynomial, we need to check if the function is made up of variables raised to non-negative whole number exponents, and if the coefficients of the terms are constants.

Step-by-step explanation:

To determine if a function is a polynomial, we need to check if the function is made up of variables raised to non-negative whole number exponents, and if the coefficients of the terms are constants. Let's analyze each function:

a) f(x) = √(x^2 + 1) - This function is not a polynomial because it contains a square root, which is not a polynomial function.

b) g(x) = x^3 + 2x^2 - 4 - This function is a polynomial because it is a sum of terms where the variables are raised to non-negative whole number exponents, and the coefficients (2 and -4) are constants.

c) h(x) = 1/x - This function is not a polynomial because it contains a variable raised to a negative exponent, which is not allowed in a polynomial function.

d) k(x) = e^x - This function is not a polynomial because it contains the exponential function e^x, which is not a polynomial function.