Combining Functions 2

Front

What is the definition of function composition?

Back

Function composition is the process of applying one function to the results of another function. If f(x) and g(x) are two functions, then the composition of f and g is denoted as f(g(x)).

Front

What does g(f(2)) represent in function composition?

Back

g(f(2)) represents the value of the function g evaluated at the output of the function f when the input is 2.

Front

How do you find (f - g)(x)?

Back

To find (f - g)(x), subtract the function g(x) from f(x): (f - g)(x) = f(x) - g(x).

Front

What is the result of (f + g)(x)?

Back

To find (f + g)(x), add the function g(x) to f(x): (f + g)(x) = f(x) + g(x).

Front

What is the domain of a function?

Back

The domain of a function is the set of all possible input values (x-values) for which the function is defined.

Front

How do you determine the domain of G/F?

Back

To determine the domain of G/F, identify the values of x for which the function G is defined and ensure that F(x) is not equal to zero.

Front

What is a linear function?

Back

A linear function is a function that can be graphically represented as a straight line, typically in the form f(x) = mx + b, where m is the slope and b is the y-intercept.

Front

What is a parabolic function?

Back

A parabolic function is a quadratic function that can be represented in the form f(x) = ax^2 + bx + c, where a, b, and c are constants.

Front

What does it mean for a function to be defined at a point?

Back

A function is defined at a point if there is a corresponding output value for that input value in the function.

Front

What is the significance of evaluating f(g(0))?

Back

Evaluating f(g(0)) means finding the output of g at 0 and then using that output as the input for the function f.