Basics of Functions and Their Properties

What is a function?

• A function is a random assignment of outputs to inputs.

• A function is a type of variable in programming.

• A function is a relation that assigns exactly one output for each input.

• A function is a collection of unrelated values.

Define the domain and range of a function.

• Domain: set of all output values; Range: set of all input values.

• Domain: set of all possible values; Range: set of all possible inputs.

• Domain: set of all possible input values; Range: set of all possible output values.

• Domain: set of all real numbers; Range: set of all integers.

What is the notation for a function?

• f(x) or g(a, b)

• h(x,y,z)

• function(x)

• f{y}

Explain what a composite function is.

• A composite function is a function created by combining two functions, where the output of one function becomes the input of another.

• A composite function is a function that cannot be broken down into simpler functions.

• A composite function is a function that only takes a single input.

• A composite function is the sum of two functions.

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

• 5

• 9

• 4

• 7

What is the inverse of a function?

• A function that increases the output of the original function.

• A function that only applies to positive numbers.

• A function that has the same effect as the original function.

• A function that reverses the effect of the original function.

How do you find the inverse of a function algebraically?

• Graph the function and reflect it over the line y=x.

• To find the inverse of a function, replace f(x) with y, swap x and y, solve for y, and then replace y with f⁻¹(x).

• Replace f(x) with x, swap x and y, and solve for x.

• Differentiate the function and then swap the variables.

If g(x) = x^2, is g(x) one-to-one? Why or why not?

• No, g(x) is one-to-one because it is a polynomial function.

• g(x) is one-to-one since it passes the horizontal line test.

• No, g(x) is not one-to-one.

• Yes, g(x) is one-to-one because it is a linear function.

What is the composition of functions f and g, denoted as (f ∘ g)(x)?

• (f ∘ g)(x) = g(x) + f(x)

• (f ∘ g)(x) = g(f(x))

• (f ∘ g)(x) = f(g(x))

• (f ∘ g)(x) = f(x) - g(x)

If f(x) = x + 1 and g(x) = 3x, what is (f ∘ g)(2)?

• 4

• 5

• 7

• 9