Flashcard 4A

Front

What is the composition of functions?

Back

The composition of functions, denoted as (f ° g)(x), is the application of one function to the results of another. It is defined as (f ° g)(x) = f(g(x)).

Front

Calculate (f ° f)(-2) for f(x) = 2x² - 1.

Back

(f ° f)(-2) = 97.

Front

What is the value of f(g(3)) if f(x) = 2x and g(x) = 2x² - 1?

Back

f(g(3)) = 34.

Front

How do you find f(g(2)) using a graph of functions f and g?

Back

Evaluate g(2) first, then substitute that result into f.

Front

What is the sum of two functions f(x) = 3x² - 4 and g(x) = x² - 8x + 4?

Back

(f + g)(x) = 4x² - 8x.

Front

Define a function. What are its key characteristics?

Back

A function is a relation that assigns exactly one output for each input. Key characteristics include domain, range, and the rule that defines the relationship.

Front

What does it mean for a function to be undefined?

Back

A function is undefined at a point if there is no valid output for that input, often due to division by zero or taking the square root of a negative number.

Front

Explain the concept of a quadratic function.

Back

A quadratic function is a polynomial function of degree 2, typically in the form f(x) = ax² + bx + c, where a, b, and c are constants.

Front

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

Back

The vertex of a quadratic function is the highest or lowest point on the graph, representing the maximum or minimum value of the function.

Front

How do you determine the roots of a quadratic function?

Back

The roots of a quadratic function can be found using the quadratic formula: x = (-b ± √(b² - 4ac)) / (2a).