The video tutorial explores functions, their relation to coordinates, and solving equations by working backwards. It begins with evaluating h(x) = 2x for values between 0 and 3, finding corresponding coordinates. Next, it demonstrates solving f(x) = 3x + 1 for C when f(C) = 31, using algebraic manipulation. Finally, it covers solving G(x) = 2x^2 + 2 for B when G(B) = 34, highlighting the importance of considering both positive and negative roots.

What is the main focus of the video?

• Studying geometry

• Learning about integrals

• Exploring functions and their applications

• Understanding derivatives

What is the value of h(0) for the function h(x) = 2x?

• 1

• 0

• 2

• 3

What coordinate is obtained when x = 1 for h(x) = 2x?

• (1, 1)

• (1, 0)

• (1, 2)

• (1, 3)

For h(x) = 2x, what is the output when x = 3?

• 6

• 5

• 3

• 4

What is the value of C if f(C) = 31 for the function f(x) = 3x + 1?

• 11

• 12

• 10

• 9

In the function f(x) = 3x + 1, what is the result of f(10)?

• 32

• 31

• 33

• 30

What operation is performed to isolate C in the equation 3C + 1 = 31?

• Addition

• Subtraction

• Multiplication

• Division

What is the value of B if g(B) = 34 for the function g(x) = 2x^2 + 2?

• 2

• 4

• 3

• 5

What is the result of g(4) for the function g(x) = 2x^2 + 2?

• 34

• 36

• 38

• 32

What is the first step in solving 2B^2 + 2 = 34?

• Divide both sides by 2

• Multiply both sides by 2

• Add 2 to both sides

• Subtract 2 from both sides