Understanding Rational Functions

What does the term 'rational' typically imply in the context of functions?

• A whole number

• A decimal

• A fraction

• An integer

What is the parent function for rational functions discussed in the lesson?

• f(x) = x + 1

• f(x) = x^2

• f(x) = 1/x

• f(x) = x - 1

Why is x = 0 not included in the domain of the function f(x) = 1/x?

• Because it results in an undefined value

• Because it results in a positive number

• Because it results in a negative number

• Because it results in a zero value

What is the domain of the function f(x) = 1/x in interval notation?

• (-∞, ∞)

• (-∞, 0) ∪ (0, ∞)

• [0, ∞)

• (-∞, 0]

What is the range of the function f(x) = 1/x in interval notation?

• (-∞, 0]

• [0, ∞)

• (-∞, ∞)

• (-∞, 0) ∪ (0, ∞)

What does a vertical stretch in a rational function graph involve?

• Changing the y-values

• Changing both x and y values

• No change in values

• Changing the x-values

How does a horizontal stretch affect the graph of a rational function?

• It stretches the graph vertically

• It compresses the graph vertically

• It stretches the graph horizontally

• It compresses the graph horizontally

What happens to the graph of f(x) = 1/x if a negative sign is introduced in front of the function?

• The graph shifts downwards

• The graph shifts upwards

• The graph reflects over the x-axis

• The graph reflects over the y-axis

In the context of rational functions, what does the term 'asymptote' refer to?

• A line that the graph approaches but never touches

• A point where the graph crosses the axis

• A line that the graph always touches

• A point where the graph intersects itself

What is the effect of adding a constant to the function f(x) = 1/x?

• It compresses the graph

• It stretches the graph

• It shifts the graph vertically

• It shifts the graph horizontally