Understanding Functions and Graphs

The video tutorial covers several math problems, including calculating the time it takes for two airplanes traveling in opposite directions to be a certain distance apart, determining the amount of pure fruit juice needed to achieve a specific concentration in a mixture, understanding the concept of functions, and identifying equations with all negative y values. The tutorial emphasizes practical applications of algebra and functions, providing step-by-step solutions and explanations.

Two airplanes leave the same airport traveling in opposite directions. One averages 400 mph and the other 250 mph. How long will it take for them to be 1625 miles apart?

• 3 hours

• 3.5 hours

• 2 hours

• 2.5 hours

If you are on one of the airplanes and consider yourself stationary, how fast does the other airplane appear to be moving away from you?

• 400 mph

• 1625 mph

• 250 mph

• 650 mph

Lisa wants to make a punch that is 25% fruit juice by adding pure fruit juice to a 2-liter mixture that is 10% fruit juice. How much pure fruit juice should she add?

• 0.2 liters

• 0.4 liters

• 0.6 liters

• 0.8 liters

What is the total amount of fruit juice in the mixture after adding the pure fruit juice?

• 0.6 liters

• 0.8 liters

• 0.4 liters

• 0.2 liters

In the context of functions, what is the key characteristic that defines a function?

• Each input has multiple outputs

• Each input has exactly one output

• Each output has multiple inputs

• Each output has exactly one input

Which of the following is NOT a function?

• A relation where each input has a unique output

• A relation where one input maps to two different outputs

• A relation where two inputs map to the same output

• A relation where each output has a unique input

Which graph represents an equation where all y-values are negative?

• A graph entirely below the x-axis

• A graph with both positive and negative y-values

• A graph crossing the x-axis

• A graph entirely above the x-axis

If a graph stays entirely in the third and fourth quadrants, what can be said about its y-values?

• Y-values are both positive and negative

• All y-values are negative

• All y-values are positive

• Y-values are zero