Function Operations

Front

What is the definition of function addition?

Back

Function addition is the operation of adding two functions together, defined as (f + g)(x) = f(x) + g(x) for all x in the domain of f and g.

Front

How do you find (f + g)(x) for two functions f(x) and g(x)?

Back

To find (f + g)(x), you evaluate f(x) and g(x) separately and then add the results together: (f + g)(x) = f(x) + g(x).

Front

What is the definition of function subtraction?

Back

Function subtraction is the operation of subtracting one function from another, defined as (f - g)(x) = f(x) - g(x) for all x in the domain of f and g.

Front

How do you find (f - g)(x) for two functions f(x) and g(x)?

Back

To find (f - g)(x), you evaluate f(x) and g(x) separately and then subtract g(x) from f(x): (f - g)(x) = f(x) - g(x).

Front

What is the standard form of a quadratic function?

Back

The standard form of a quadratic function is f(x) = ax^2 + bx + c, where a, b, and c are constants and a ≠ 0.

Front

What is the degree of a polynomial function?

Back

The degree of a polynomial function is the highest power of the variable in the polynomial. For example, in f(x) = 3x^2 + 2x + 1, the degree is 2.

Front

What is the result of adding two quadratic functions?

Back

The result of adding two quadratic functions is another quadratic function, which can be expressed in the form f(x) + g(x) = (a1 + a2)x^2 + (b1 + b2)x + (c1 + c2).

Front

What is the result of subtracting two quadratic functions?

Back

The result of subtracting two quadratic functions is another quadratic function, which can be expressed in the form f(x) - g(x) = (a1 - a2)x^2 + (b1 - b2)x + (c1 - c2).

Front

What is the significance of the coefficients in a quadratic function?

Back

The coefficients in a quadratic function determine the shape and position of the parabola represented by the function. The coefficient 'a' affects the direction and width, while 'b' and 'c' affect the position.

Front

How do you combine like terms when adding or subtracting polynomials?

Back

To combine like terms, group the terms with the same degree and add or subtract their coefficients. For example, 3x^2 + 2x^2 = 5x^2.