Q: Which of the following best describes the end behavior of the function in the third image ($$y = x^3$)?

$$y \to \infty as$$ $$x \to \infty$$ and $$y \to -\infty as$$ $$x \to -\infty$$

Question 1

Which of the following graphs best represents the function $$f(x) = x^3$?

Accepted Answer

The third image (an S-shaped curve passing through the origin)

Question 2

Suppose $$f(t)$$ represents the profit of a company over time, as shown in the first image. At which labeled point does the company experience a local minimum in profit?

Accepted Answer

$$(b, f(b))$$

Question 3

Which of the following equations best describes the graph in the fourth image?

Accepted Answer

$$y = -x^2$

Question 4

The graph in the sixth image shows a function $$H(t)$$ that models the amount of a drug in the bloodstream over time. What is the long-term behavior of $$H(t) as$$ $$t$$ increases?

Accepted Answer

$$H(t)$$ approaches a constant value (levels off)

Question 5

Which graph best represents a function with a global maximum at $$x = 0$$?

Accepted Answer

The fifth image (downward-opening parabola)

Question 6

If the graph in the second image represents $$y = -x^3$, which of the following statements is true?

Accepted Answer

The function is decreasing for all $$x$$

Question 7

Given the graph in the first image, which labeled point is most likely to be an inflection point?

Accepted Answer

$$(c, f(c))$$

Question 8

Which of the following best describes the end behavior of the function in the third image ($$y = x^3$)?

Accepted Answer

$$y 	o \infty as$$ $$x 	o \infty$$ and $$y 	o -\infty as$$ $$x 	o -\infty$$

Question 9

If the graph in the sixth image models the cooling of a hot object, which law does it most closely follow?

Accepted Answer

Newton's Law of Cooling

Question 10

Which of the following graphs represents a function with a minimum at $$x = 0$$?

Accepted Answer

The fourth image (upward-opening parabola)

Question 11

Suppose the graph in the first image represents the cost of production over time. At which labeled point is the marginal cost zero?

Accepted Answer

At points where the tangent is horizontal, such as $$(a, f(a))$$ and $$(c, f(c))$$

Question 12

Which of the following best describes the concavity of the function in the fourth image?

Accepted Answer

Concave down for all $$x$$

Question 13

If the function in the sixth image is $$H(t) = 200(1 - e$$^{-0.05t}$$)$$, what is the horizontal asymptote?

Accepted Answer

$$y = 200$$

Question 14

Which graph best represents a function that is always increasing?

Accepted Answer

The third image ($$y = x^3$)

Question 15

If the graph in the second image is $$y = -x^3$, what is the value of the derivative at x = 0$?

Accepted Answer

$$0$$

Graphs and Properties of Linear and Nonlinear Functions in Business Calculus

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