Finding Intersection Points of Functions

The video tutorial explains how to find the intersection point of two functions, f(x) = (8x + 1)/3 and g(x) = 2x + 3. It begins by setting up the equation f(x) = g(x) to find the x-coordinate of the intersection. The tutorial then demonstrates solving the equation by eliminating fractions and simplifying to find x = 4. Next, it calculates the y-coordinate by evaluating f(4) and g(4), both yielding 11, confirming the intersection point at (4, 11). The video concludes with a verification using a graphing utility.

What is the main goal of the problem discussed in the video?

• To determine the intersection point of f(x) and g(x)

• To find the maximum value of f(x)

• To calculate the derivative of g(x)

• To solve for the roots of f(x)

What is the expression for f(x) given in the video?

• 8x + 1 over 3

• 2x + 3

• 4x - 5

• x^2 + 2x + 1

What is the expression for g(x) given in the video?

• 4x - 5

• x^2 + 2x + 1

• 8x + 1 over 3

• 2x + 3

What is the first step in solving the equation f(x) = g(x)?

• Divide both sides by 2

• Subtract 2x from both sides

• Multiply both sides by 3

• Add 5 to both sides

After eliminating the fraction, what does the left side of the equation become?

• 4x - 5

• 2x + 3

• 8x + 1

• 6x + 9

What is the result after subtracting 6x from both sides of the equation?

• x = 2

• 2x = 8

• 4x = 10

• x = 4

What is the x-coordinate of the intersection point?

• 2

• 3

• 4

• 5

How do you find the y-coordinate of the intersection point?

• By setting f(x) to zero

• By finding the derivative of g(x)

• By solving for x in f(x)

• By evaluating f(4) or g(4)

What is the value of f(4)?

• 12

• 11

• 13

• 10

What is the value of g(4)?

• 13

• 12

• 11

• 10