Operations with Functions

Front

Define a function.

Back

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

Front

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

Back

The sum of two functions f(x) and g(x) is defined as (f+g)(x) = f(x) + g(x).

Front

Evaluate the function h(x) = 3x + 1 at x = 4.

Back

h(4) = 3(4) + 1 = 13.

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

If f(x) = 2x + 3, what is f(0)?

Back

f(0) = 2(0) + 3 = 3.

Front

What does it mean for a function to be linear?

Back

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

Front

Find f(n) + g(n) if f(n) = n^2 + 4n and g(n) = -n - 5.

Back

f(n) + g(n) = n^2 + 4n - n - 5 = n^2 + 3n - 5.

Front

What is the definition of 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

Evaluate h(x) = 2x + 2 at x = -7.

Back

h(-7) = 2(-7) + 2 = -14 + 2 = -12.

Front

If f(x) = 9 - 3x and g(x) = 5x - 7, what is f(x) + g(x)?

Back

f(x) + g(x) = (9 - 3x) + (5x - 7) = 2x + 2.