Function Characteristics and Water Flow Problems

The video tutorial covers linear functions and their properties, focusing on proportionality and constant rates of change. It includes exercises on graphing linear functions, analyzing a candy cost function, calculating water flow rates, and determining running distances. The tutorial emphasizes understanding the concept of slope and its application in real-world scenarios.

What is a key characteristic of a function in terms of inputs and outputs?

• Each input maps to multiple outputs.

• Each input maps to only one output.

• Each output maps to only one input.

• Each output maps to multiple inputs.

How can the rate of change in a function be described?

• As the difference between outputs.

• As the difference between inputs.

• As the slope of the function.

• As the sum of inputs and outputs.

What does a constant rate of change indicate about a graph?

• The graph is a circle.

• The graph is a curve.

• The graph is a straight line.

• The graph is a zigzag.

In the water flow example, what is the rate of water flow from the faucet?

• 7 gallons per minute

• 3.5 gallons per minute

• 7 gallons per 2 minutes

• 3.5 gallons per 2 minutes

How long will it take to fill a 50-gallon tub with a flow rate of 3.5 gallons per minute?

• 15 minutes

• 14.3 minutes

• 13.5 minutes

• 16 minutes

What is the initial condition in the third exercise regarding water in the tub?

• The tub is empty.

• The tub has 6 gallons of water.

• The tub has 8 gallons of water.

• The tub is full.

How many minutes before noticing did the faucet start dripping if there were 6 gallons in the tub?

• 6 minutes

• 4 minutes

• 3 minutes

• 5 minutes

What is the slope of Veronica's running distance function?

• 1/2

• 1/8

• 1/16

• 1/4

How far can Veronica run in 180 minutes?

• 18 miles

• 25 miles

• 22.5 miles

• 20 miles