Question

The sum and product of two linear functions are shown. Which statements can be used to describe the original functions f(x) and g(x)? Select two options.

A) The sum of the two functions yields a quadratic function.
B) The product of the two functions yields a linear function.
C) Both functions f(x) and g(x) must be quadratic functions.
D) One of the functions must be linear, and the other must be quadratic.

Answer 1

The original functions f(x) and g(x) can be described using the statements: one of the functions must be linear, and the other must be quadratic, and the sum of the two functions yields a quadratic function.

Step-by-step explanation:

The statements that can be used to describe the original functions f(x) and g(x) are:

• Option A) The sum of the two functions yields a quadratic function. This statement is not true. The sum of two linear functions will always yield another linear function.
• Option B) The product of the two functions yields a linear function. This statement is also not true. The product of two linear functions will yield a quadratic function.
• Option C) Both functions f(x) and g(x) must be quadratic functions. This statement is not true. The sum and product of two linear functions can never be quadratic functions.
• Option D) One of the functions must be linear, and the other must be quadratic. This statement is correct. The sum of a linear function and a quadratic function will always yield a quadratic function.

Therefore, options D and A are the correct statements to describe the original functions f(x) and g(x).