Analyzing Graphs of Rational Functions

What values of x are not allowed in the function's domain?

• x = 3 and x = -2

• x = 0

• x = 1 and x = -1

• x = 2 and x = -3

What is the horizontal asymptote of the function?

• y = 1

• y = 0

• y = x

• y = -1

Where is the x-intercept of the function located?

• x = 2

• x = -1

• x = 1

• x = 0

What is the y-intercept of the function?

• 1

• -1/6

• 0

• 1/6

What happens to the function as x approaches -2 from the left?

• Remains constant

• Approaches zero

• Approaches negative infinity

• Approaches positive infinity

What is the behavior of the function as x approaches 3 from the right?

• Approaches negative infinity

• Approaches zero

• Remains constant

• Approaches positive infinity

As x goes to negative infinity, the function approaches what value?

• -1

• 0

• Infinity

• 1

What is the vertical asymptote of the new function introduced?

• x = 0

• x = -1

• x = 1

• x = 2

What type of asymptote is described by the quotient x^2 - 2x + 1?

• Oblique asymptote

• None of the above

• Vertical asymptote

• Horizontal asymptote

For the function f(x) = x^3 - 3x^2 + 3x + 1 over x - 1, what is the correct division result?

• x^2 - x + 1 + 2/(x - 1)

• x^2 + 2x + 1 + 2/(x - 1)

• x^2 - 2x - 1 + 2/(x - 1)

• x^2 - 2x + 1 + 2/(x - 1)