Graphing Rational Functions: Key Concepts and Techniques

This video tutorial covers graphing rational functions, starting with the parent function f(x) = 1/x. It explains the characteristics of rational functions, including undefined values and asymptotes. The tutorial demonstrates how to graph the parent function and introduces transformations to graph other rational functions. Examples are provided to illustrate the application of transformations, including shifts and reflections, to create new graphs.

What is the basic form of a rational function?

• f(x) = x + 1

• f(x) = 1/x

• f(x) = x^2

• f(x) = x - 1

What happens when x is zero in the function f(x) = 1/x?

• The function equals one

• The function equals zero

• The function is undefined

• The function equals infinity

What is a vertical asymptote?

• A line the graph crosses

• A line the graph approaches but never touches

• A point on the graph

• A horizontal line

What is the significance of a horizontal asymptote in a rational function?

• It indicates where the graph crosses the x-axis

• It indicates that the function will never reach a certain y-value

• It shows the maximum value of the function

• It shows the minimum value of the function

What is the general shape of the graph of f(x) = 1/x?

• A straight line

• A circle

• A parabola

• Two curves in opposite quadrants

What does the parameter 'a' affect in the transformation of a rational function?

• Vertical shift

• Vertical stretch or shrink

• Horizontal shift

• Horizontal stretch or shrink

If h = 2 in the function f(x) = 1/(x - h), what is the horizontal shift?

• 2 units up

• No shift

• 2 units to the right

• 2 units to the left

In the function f(x) = 1/x + k, what does the parameter 'k' represent?

• Horizontal stretch

• Vertical stretch

• Vertical shift

• Horizontal shift

What is the effect of a negative 'a' in the function f(x) = a/x?

• The graph shifts up

• The graph reflects across the y-axis

• The graph shifts down

• The graph reflects across the x-axis

In the function f(x) = 1/(x + 4), what is the vertical asymptote?

• x = -4

• x = 4

• y = -4

• y = 4