Graphing and Analyzing Functions

The video tutorial explores human space exploration, focusing on Voyager 1's launch and its speed. It introduces proportional functions, explaining their characteristics and how they relate to real-world examples like Voyager 1's journey and a Coke freezing. The tutorial covers graphing proportional functions, emphasizing the role of the constant k, and concludes by encouraging viewers to seek help with related questions.

What was the primary purpose of launching Voyager 1?

• To test new propulsion technology

• To explore the universe and gather data

• To study the Earth's atmosphere

• To explore the depths of the ocean

What is the speed of Voyager 1?

• 80,000 kilometers an hour

• 61,452 kilometers an hour

• 50,000 kilometers an hour

• 70,000 kilometers an hour

In the equation y = 61,452x, what does the constant 61,452 represent?

• The travel time

• The travel distance

• The travel speed

• The travel direction

What is a proportional function?

• A function where y is constant

• A function where y is inversely proportional to x

• A function where y is directly proportional to x

• A function where y is always zero

In the Coke freezing example, what is the rate of temperature change?

• 4 degrees Celsius per minute

• 3 degrees Celsius per minute

• 2 degrees Celsius per minute

• 1 degree Celsius per minute

What are the two conditions for a function to be proportional?

• k is positive and x is zero

• k is zero and x is squared

• k is negative and x is squared

• k is not zero and the degree of x is one

What happens to the graph of y = kx when k is positive?

• The line rises from left to right

• The line is vertical

• The line declines from left to right

• The line is horizontal

What is the effect of a negative k on the graph of y = kx?

• The line rises from left to right

• The line declines from left to right

• The line is horizontal

• The line is vertical

Which quadrants does the line y = kx pass through when k is positive?

• First and second

• First and third

• Second and third

• Third and fourth

Which points are typically used to graph a proportional function?

• Origin and point (1, k)

• Origin and point (0, 1)

• Point (1, 0) and point (0, k)

• Point (k, 1) and point (1, 0)