Identity Functions and Their Properties

The video tutorial introduces the concept of an identity function, explaining that it is a function where the domain and range are identical. The function is defined as f(x) = x, meaning for any input x, the output is the same. The tutorial provides examples with real numbers and illustrates the graph of the identity function, which is a straight line passing through the origin. The video concludes with a summary and a transition to the next type of function.

What is an identity function?

• A function where the domain and range are different

• A function where the domain and range are equal

• A function that has no output

• A function that only works with integers

Which of the following is an example of an identity function?

• f(x) = x + 1

• f(x) = 2x

• f(x) = x^2

• f(x) = x

If f(x) = x is an identity function, what is f(100)?

• 0

• 100

• 50

• 200

In an identity function, what is the output when the input is -2?

• -2

• 2

• 0

• 1

What does the graph of an identity function look like?

• A parabola

• A circle

• A straight line through the origin

• A horizontal line

Which point is NOT on the graph of an identity function?

• (-1, -1)

• (3, 4)

• (2, 2)

• (1, 1)

How can you describe the relationship between x and y in an identity function?

• y is equal to x

• y is always less than x

• y is always greater than x

• y is the square of x

What is the slope of the line representing an identity function?

• Undefined

• -1

• 1

• 0

Which of the following statements is true about identity functions?

• They map each input to itself

• They have no graphical representation

• They have a constant output

• They only work with positive numbers

What is the y-intercept of the graph of an identity function?

• -1

• 1

• 0

• It does not have a y-intercept