Week 10 Quiz

The week's parabola, f(x) = x² − 6x + 5, is a polynomial function with leading term x². Which describes its end behavior?

Select one.

• It falls on the left and rises on the right.
• It rises on both ends.
• It falls on both ends.
• It rises on the left and falls on the right.

Which describes the end behavior of −2x⁴ + 3x² − 1?

Select one.

• It rises on both ends.
• It falls on the left and rises on the right.
• It rises on the left and falls on the right.
• It falls on both ends.

The week's parabola factors as f(x) = (x − 1)(x − 5). Which statement about its zeros is right?

Select one.

• The zeros are −1 and −5, and the graph crosses at both.
• The zeros are 1 and 5, each of multiplicity 1, and the graph crosses at both.
• The zeros are 1 and 5, and the graph touches the axis at both.
• The zeros are 3 and −4, the vertex coordinates.

For (x − 1)²(x + 4), what does the graph do at x = 1?

Select one.

• It touches the x-axis and turns back, because the zero has multiplicity 2.
• It crosses the x-axis, because 1 is a zero.
• It has a vertical asymptote at x = 1.
• It crosses the x-axis and flattens, because the zero has multiplicity 3.

What are the degree and the end behavior of x²(x − 3)(x + 2)³?

Select one.

• Degree 3; it falls on the left and rises on the right.
• Degree 6; it falls on both ends.
• Degree 6; it rises on both ends.
• Degree 5; it falls on the left and rises on the right.

For R(x) = (x + 1) ⁄ (x² − 4), where are the vertical asymptotes?

Select one.

• x = −1
• x = 4
• y = 0
• x = −2 and x = 2

What happens at x = 1 on the graph of (x² − x) ⁄ (x − 1)?

Select one.

• There is a vertical asymptote x = 1.
• There is a hole at (1, 1).
• There is a hole at (1, 0).
• The graph crosses the x-axis at (1, 0).

What is the horizontal asymptote of (3x + 1) ⁄ (x − 5)?

Select one.

• y = 3
• y = 0
• y = 1⁄3
• There is no horizontal asymptote.

What is the y-intercept of R(x) = (x + 1) ⁄ (x² − 4)?

Select one.

• (0, −1⁄4)
• (−1, 0)
• (0, 1⁄4)
• (0, −4)

A print shop's average cost per tote bag is u(x) = (5x + 200) ⁄ x dollars when it makes x bags; u(10) = 25 and u(200) = 6. What does the horizontal asymptote say?

Select one.

• The average cost per bag rises toward 200 dollars.
• The average cost per bag reaches 0 dollars once enough bags are made.
• The average cost per bag falls toward 5 dollars but never reaches it.
• The average cost per bag stays at 25 dollars.

Select every function whose horizontal asymptote is y = 0.

Select every option that applies.

• (x + 1) ⁄ (x² − 4)
• 2x ⁄ (x² + 1)
• (3x + 1) ⁄ (x − 5)
• (x² + 1) ⁄ (x − 1)

True or false: the horizontal asymptote of (x² + 1) ⁄ (x − 1) is y = 1, because both leading coefficients are 1.

True or false.

• True
• False