Function Properties and Behavior

The video tutorial covers analyzing graphs of functions, focusing on domain, range, zeros, and intercepts. It explains how to describe graph behavior, calculate average rate of change, and identify even and odd functions. The tutorial also explores various parent functions and introduces piecewise and step functions.

What is the domain of a function that includes all real numbers except for x = -3?

• (-∞, -3) ∪ (-3, ∞)

• (-∞, 3) ∪ (3, ∞)

• (-∞, -3] ∪ [-3, ∞)

• (-∞, 3] ∪ [3, ∞)

Which of the following statements is true about the vertical line test?

• A graph is not a function if a vertical line never crosses it.

• A graph is a function if a vertical line never crosses it.

• A graph is not a function if a vertical line crosses it more than once.

• A graph is a function if a vertical line crosses it more than once.

How do you determine if a graph is increasing over an interval?

• The graph moves down as you trace from left to right.

• The graph moves in a circular pattern.

• The graph moves up as you trace from left to right.

• The graph remains flat as you trace from left to right.

What is the average rate of change of a function between x = -2 and x = -1 if the function values are -2 and 2 respectively?

• 0

• 4

• -4

• 2

Which of the following describes an even function?

• Exponents are a mix of even and odd.

• All exponents are even and there may be a constant.

• All exponents are odd and there is no constant.

• There is no constant and all exponents are even.

What is the parent function of a quadratic equation?

• y = x

• y = x^3

• y = 1/x

• y = x^2

How does a step function behave?

• It forms a straight line.

• It forms a series of steps.

• It forms a continuous curve.

• It forms a parabolic shape.

What is the greatest integer function?

• It rounds to the nearest odd integer.

• It rounds up to the nearest integer.

• It rounds down to the nearest integer.

• It rounds to the nearest even integer.

Which of the following is true for a function that is neither even nor odd?

• It has a mix of even and odd exponents.

• It has only even exponents.

• It has no exponents.

• It has only odd exponents.

What is the identity function?

• y = x

• y = x^2

• y = x^3

• y = 1/x