Understanding Function Properties

The video tutorial explains how to define a function f(x) = ax^3 + b, where a and b are constants. It uses given conditions f(0) = 2 and f(2) = 3 to determine the values of a and b. The tutorial demonstrates solving for b as 2 and a as 1/8, and verifies that a > 0, b > 0, and a < b are true.

What is the general form of the function f(x) as defined in the video?

• f(x) = ax + b

• f(x) = ax^3 + b

• f(x) = ax^3 + bx

• f(x) = ax^2 + b

If f(0) = 2, what does this tell us about the constant b?

• b = 3

• b = 2

• b = 1

• b = 0

What is the value of f(0) in terms of a and b?

• 0

• a + b

• b

• a

What equation is formed when substituting f(2) = 3 into the function?

• 8a + 2 = 3

• 2a + b = 3

• 8a + b = 3

• 4a + b = 3

How do you solve for a when given the equation 8a + 2 = 3?

• Multiply both sides by 8, then subtract 2

• Add 2 to both sides, then divide by 8

• Divide both sides by 8, then add 2

• Subtract 2 from both sides, then divide by 8

What is the value of a after solving the equation 8a + 2 = 3?

• 1

• 1/8

• 1/2

• 1/4

Which of the following is true about the constants a and b?

• a is greater than b

• a is greater than zero

• a is less than b

• a is equal to b

What is the relationship between a and zero?

• a is less than zero

• a is equal to zero

• a is not related to zero

• a is greater than zero

Which of the following statements is true about b?

• b is less than zero

• b is not related to zero

• b is equal to zero

• b is greater than zero