Understanding Rational Functions and Transformations

The video tutorial covers graphing rational functions, focusing on the reciprocal function 1/x. It explains the concept of rational functions, graphing techniques, and key characteristics like asymptotes. The tutorial also delves into transformations, including horizontal and vertical shifts, reflections, and stretches. Finally, it guides viewers on writing equations for transformed functions and identifying asymptotes.

What is a rational function?

• A function that is always linear.

• A function that can be expressed as a polynomial.

• A function that is the sum of two polynomials.

• A function that is the ratio of two polynomials.

What is the parent function of a rational function?

• f(x) = 1/x

• f(x) = x^2

• f(x) = x + 1

• f(x) = x^3

What happens to the graph of f(x) = 1/x at x = 0?

• It reaches a maximum point.

• It is undefined and forms an asymptote.

• It becomes a straight line.

• It crosses the x-axis.

What is the effect of a negative 'a' value in a rational function transformation?

• It compresses the graph vertically.

• It reflects the graph across the x-axis.

• It stretches the graph horizontally.

• It shifts the graph to the right.

How does a positive 'k' value affect the graph of a rational function?

• It compresses the graph horizontally.

• It shifts the graph down.

• It shifts the graph up.

• It reflects the graph across the y-axis.

What is the vertical asymptote of f(x) = 1/(x - 5) - 2?

• x = 5

• x = -5

• x = 2

• x = 0

If a rational function is translated 4 units right, what happens to the denominator?

• x + 4

• x - 1

• x + 1

• x - 4

What is the horizontal asymptote of a function with a k value of -3?

• y = 1

• y = -3

• y = 3

• y = 0

How is the function f(x) = 1/(x + 2) + 5 transformed from the parent function?

• Shifted left 2 units and up 5 units

• Shifted right 2 units and down 5 units

• Shifted right 2 units and up 5 units

• Shifted left 2 units and down 5 units

What is the effect of a vertical stretch by a factor of 2 on a rational function?

• It doubles the x-values.

• It halves the y-values.

• It doubles the y-values.

• It halves the x-values.