DMAC Properties of Functions

Susan purchased one large cheese pizza to be shared with her friends. Susan and each of her friends will get an equal share of the pizza. The portion of the pizza that each person will get can be represented by the function f(x) = 1/x where x represents the number of people sharing the pizza. What is the portion of the pizza each person will receive if there are 4 people sharing the pizza?

• 1/2

• 1/3

• 1/4

• 1/5

Determine the domain and range in terms of the problem situation. Represent the domain and range in inequality, set, and interval notation.

• Domain: x ≥ 0, Range: y ≥ 0

• Domain: x ≤ 0, Range: y ≤ 0

• Domain: x > 0, Range: y > 0

• Domain: x < 0, Range: y < 0

Analyze the graph to identify the asymptotic behavior of the function. Describe this behavior in terms of the problem situation.

• The function approaches a horizontal asymptote.

• The function approaches a vertical asymptote.

• The function has no asymptotic behavior.

• The function oscillates indefinitely.

In order to test a new medication at a research laboratory, a rat was injected with 1 gram of the medication. Data was then collected to determine the amount of medication in grams left in the rat’s blood stream at the end of each hour. The grams of medication in the rat’s blood stream, A(t), as a function of time in hours, t, is given as A(t) = (1/2)^t. What is the amount of medication left in the rat's bloodstream after 3 hours?

• 0.125 grams

• 0.25 grams

• 0.5 grams

• 1 gram

In order to test a new medication at a research laboratory, a rat was injected with 1 gram of the medication. Data was then collected to determine the amount of medication in grams left in the rat’s blood stream at the end of each hour. The grams of medication in the rat’s blood stream, A(t), as a function of time in hours, t, is given as A(t) = (1/2)^t. Part B Which of the following represents the domain and range in terms of the problem situation?

• Domain: t ≥ 0; Range: 0 < A(t) ≤ 1

• Domain: t > 0; Range: 0 ≤ A(t) < 1

• Domain: t ≤ 0; Range: A(t) ≥ 1

• Domain: t < 0; Range: A(t) > 1

In order to test a new medication at a research laboratory, a rat was injected with 1 gram of the medication. Data was then collected to determine the amount of medication in grams left in the rat’s blood stream at the end of each hour. The grams of medication in the rat’s blood stream, A(t), as a function of time in hours, t, is given as A(t) = (1/2)^t. Part C Analyze the graph to identify the y-intercept and asymptotic behavior of the function. Describe each in terms of the problem situation.

• The y-intercept is 1 gram, and the asymptote is y = 0.

• The y-intercept is 0.5 grams, and the asymptote is y = 1.

• The y-intercept is 1 gram, and the asymptote is y = 1.

• The y-intercept is 0 grams, and the asymptote is y = 0.

Which symmetry is represented by the function f(x) = |x|?

• Rotational symmetry of 90°

• Reflectional symmetry in the x-axis

• Reflectional symmetry in the y-axis

• Rotational symmetry of 180°

Which statement best describes the asymptotic behavior of the graph of the function f(x) = log x?

• The graph of f(x) = log x approaches and crosses the line y = 2.

• The graph of f(x) = log x approaches and does not cross the line x = 0.

Which symmetry is represented by the function f(x) = \sqrt[3]{x}?

• Rotational symmetry of 90°

• Reflectional symmetry in the x-axis

• Reflectional symmetry in the y-axis

• Rotational symmetry of 180°

What is the intercept(s) of the function f(x) = x^3?

• (0, 0)

• (−1, 0) and (0, 0)

• (1, 0) and (0, 0)

• −0.5 < x < 0.5