Understanding Linear and Exponential Functions

The video tutorial explains the graphs of a linear function and an exponential function, both passing through the points (-1, 9) and (1, 1). It derives the equation of the linear function by calculating the slope and y-intercept, resulting in f(x) = -4x + 5. The exponential function is analyzed using the given points, leading to the equation g(x) = 3 * (1/3)^x. The tutorial emphasizes understanding the behavior of these functions and their graphical representations.

What is the general form of a linear function?

• f(x) = x^2 + y^2

• f(x) = ax^2 + bx + c

• f(x) = mx + b

• f(x) = a * r^x

Which of the following points does the linear function pass through?

• (1, 1)

• (3, 5)

• (2, 3)

• (0, 0)

How do you calculate the slope of a line given two points?

• Subtract the y-coordinates

• Divide the change in y by the change in x

• Multiply the x and y coordinates

• Add the x-coordinates

What is the slope of the linear function in the video?

• 0

• -4

• 1

• 2

What is the y-intercept of the linear function?

• 3

• 5

• 6

• 4

What is the general form of an exponential function?

• g(x) = mx + b

• g(x) = x^2 + y^2

• g(x) = ax^2 + bx + c

• g(x) = a * r^x

Which point is used to set up the first equation for the exponential function?

• (0, 0)

• (-1, 9)

• (1, 1)

• (2, 3)

What is the value of r in the exponential function?

• 1/2

• 1/5

• 1/3

• 1/4

What is the value of a in the exponential function?

• 4

• 3

• 2

• 5

What is the final form of the exponential function?

• g(x) = 2 * (1/3)^x

• g(x) = 3 * (1/3)^x

• g(x) = 2 * (1/2)^x

• g(x) = 3 * (1/2)^x