Exploring Key Features of Functions

Mr. Murphy introduces key features of functions, focusing on domain, range, and notation. He explains domain and range using examples, including a quadratic function. The video covers set builder and interval notation, demonstrating their use in describing intervals. Mr. Murphy also discusses x and y intercepts, providing examples and exercises for practice.

What is the domain of the function y = x^2 - 3?

• All integers

• All negative numbers

• All positive numbers

• All real numbers

What is the smallest possible value of the function y = x^2 - 3?

• -1

• 3

• -3

• 0

Which notation uses verbal descriptions or inequalities to describe numbers?

• Function notation

• Set builder notation

• Graphical notation

• Interval notation

In interval notation, what symbol is used to represent that a boundary is included?

• Bracket

• Parenthesis

• Colon

• Comma

If an airtanker releases water at a rate of 400 gallons per second and has a capacity of 8000 gallons, what is the maximum time it can release water?

• 40 seconds

• 30 seconds

• 20 seconds

• 10 seconds

What is the range of the airtanker's water release function?

• 0 to 400 gallons

• 0 to 8000 gallons

• 0 to 20 seconds

• 400 to 8000 gallons

What is the x-intercept of the function y = 16 - 0.05x?

• (16, 0)

• (0, 16)

• (320, 0)

• (0, 320)

What does the y-intercept of the function y = 16 - 0.05x represent in the context of a car's fuel consumption?

• The car's fuel efficiency

• The initial amount of fuel

• The car's maximum speed

• The distance traveled

For the function y = |x - 3|, what are the x-intercepts?

• 3 and 0

• 0 and 3

• 3 and -3

• 3 and -3

In which interval is the function y = x^2 - 4 positive?

• (-∞, 2)

• (-∞, -2) and (2, ∞)

• (-2, 2)

• (2, ∞)