Evaluating Functions and Expressions

Front

What is a function?

Back

A function is a relation between a set of inputs and a set of possible outputs where each input is related to exactly one output.

Front

Evaluate f(x) = x^2 for f(-8).

Back

64

Front

What is the sum of two functions f(x) and g(x)?

Back

The sum of two functions, denoted as (f + g)(x), is found by adding their outputs: (f + g)(x) = f(x) + g(x).

Front

Given f(x) = 3x^2 + 7x and g(x) = 2x^2 - x - 1, find (f + g)(x).

Back

5x^2 + 6x - 1

Front

What is function composition?

Back

Function composition is the process of applying one function to the results of another function, denoted as (g ∘ f)(x) = g(f(x)).

Front

Evaluate g(f(x)) for f(x) = x^2 and g(x) = 2x + 3.

Back

2x^2 + 3

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

What is the range of a function?

Back

The range of a function is the set of all possible output values (y-values) that the function can produce.

Front

What does it mean for a function to be linear?

Back

A function is linear if it can be expressed in the form f(x) = mx + b, where m and b are constants.

Front

What is a quadratic function?

Back

A quadratic function is a polynomial function of degree 2, typically in the form f(x) = ax^2 + bx + c.