Understanding Rational Functions

The video tutorial explains how to find a rational function in the form of a reciprocal function that passes through given points. It covers transformations, vertical and horizontal asymptotes, and graph properties based on the value of 'a'. The tutorial demonstrates solving for variables A and K using a system of equations and verifies the solution by checking the function with the given points.

What is the parent function of a reciprocal function?

• 1 over X

• X squared

• X plus 1

• X minus 1

What does the variable 'H' represent in the function a/(x-h) + k?

• Slope of the line

• Vertical asymptote

• Y-intercept

• Horizontal asymptote

If 'a' is negative, how does the graph of the function behave?

• It remains unchanged

• It reflects across the x-axis

• It shrinks

• It stretches

What happens to the graph if the absolute value of 'a' is greater than 1?

• The graph shifts

• The graph shrinks

• The graph stretches

• The graph reflects

What is the first step in solving for A and K using the given points?

• Find the asymptotes

• Graph the points

• Calculate the slope

• Form two equations

How do you eliminate the fraction in the equation 4 = a/(1-3) + k?

• Add 2 to both sides

• Subtract 2 from both sides

• Divide by 2

• Multiply by -2

What is the value of 'a' after solving the system of equations?

• 5

• 4

• 3

• 2

What is the final form of the function that passes through the points?

• Y = 4/(x-3) + 6

• Y = 3/(x-2) + 5

• Y = 5/(x-4) + 7

• Y = 6/(x-5) + 8

How can you verify the correctness of the derived function?

• By plugging in the x-values of the points

• By calculating the slope

• By graphing the function

• By checking the asymptotes

What is the y-value when x = 5 in the derived function?

• 4

• 6

• 10

• 8