Starter Activity: Function Operations

Front

What is function addition?

Back

Function addition involves combining two functions, f(x) and g(x), to create a new function (f + g)(x) = f(x) + g(x).

Front

How do you find (f + g)(x) for f(x) = 3x² + 7x and g(x) = 2x² - x - 1?

Back

(f + g)(x) = (3x² + 7x) + (2x² - x - 1) = 5x² + 6x - 1.

Front

What is function subtraction?

Back

Function subtraction involves subtracting one function from another, resulting in (f - g)(x) = f(x) - g(x).

Front

How do you find (f - g)(x) for f(x) = 3x² + 7x and g(x) = 2x² - x - 1?

Back

(f - g)(x) = (3x² + 7x) - (2x² - x - 1) = x² + 8x + 1.

Front

What is function multiplication?

Back

Function multiplication involves multiplying two functions together, resulting in (f * g)(x) = f(x) * g(x).

Front

How do you find (f * g)(x) for f(x) = 3x² - 2x + 1 and g(x) = x - 4?

Back

(f * g)(x) = (3x² - 2x + 1)(x - 4) = 3x³ - 14x² + 9x - 4.

Front

What is the degree of a polynomial?

Back

The degree of a polynomial is the highest power of the variable in the polynomial.

Front

What is the leading coefficient of a polynomial?

Back

The leading coefficient is the coefficient of the term with the highest degree in a polynomial.

Front

What is a polynomial function?

Back

A polynomial function is a function that can be expressed in the form f(x) = a_nx^n + a_(n-1)x^(n-1) + ... + a_1x + a_0, where a_n are constants and n is a non-negative integer.

Front

What is the standard form of a polynomial?

Back

The standard form of a polynomial is written in descending order of the degree of its terms.