M647 Function Operations

Front

Define 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) = f(g(x)).

Front

What is the formula for finding (f + g)(x)?

Back

The formula for finding (f + g)(x) is (f + g)(x) = f(x) + g(x).

Front

Calculate f(g(x)) when f(x) = 2x and g(x) = x^2 + 3.

Back

f(g(x)) = 2(x^2 + 3) = 2x^2 + 6.

Front

What is the result of f(x) - g(x) if f(x) = x^2 + 9 and g(x) = x - 9?

Back

f(x) - g(x) = (x^2 + 9) - (x - 9) = x^2 - x + 18.

Front

How do you find (g ∘ h)(x) for g(x) = 3x + 4 and h(x) = 3x - 1?

Back

(g ∘ h)(x) = g(h(x)) = g(3x - 1) = 3(3x - 1) + 4 = 9x + 1.

Front

What is the definition of the term 'function'?

Back

A function is a relation that assigns exactly one output for each input from a set of inputs, called the domain.

Front

Explain the concept of 'domain' in functions.

Back

The domain of a function is the complete set of possible values of the independent variable (input) for which the function is defined.

Front

What is the range of a function?

Back

The range of a function is the set of all possible output values (dependent variable) that result from using the function.

Front

Define the term 'linear function'.

Back

A linear function is a function that can be graphically represented in the Cartesian plane as a straight line, typically in the form f(x) = mx + b.

Front

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

Back

In a quadratic function of the form f(x) = ax^2 + bx + c, 'a' determines the direction of the parabola, 'b' affects the position of the vertex, and 'c' is the y-intercept.