H Unit 2 Review: Functions

Which best describes the relationship between the successive terms in the sequence shown?

2.4, –4.8, 9.6, –19.2

• The common difference is –7.2.

• The common difference is –2.4.

• The common ratio is –2.0.

• The common ratio is –0.5.

Mr. Jones asks his students to generate the next two numbers in the sequence beginning –5.5, 11, ....

Taquan suggests that the sequence is geometric and the next two numbers are –22 and 44. Julia suggests that the sequence is arithmetic and the next two numbers are 27.5 and 44.

Which best explains which student is correct?

• Taquan is correct. When the signs change in a sequence, the sequence is geometric. Each successive term is generated by multiplying by –22 .

• Julia is correct. When the numbers alternate between decimals and whole numbers, the sequence is arithmetic. Each successive term is generated by adding 16.5

• Both students could be correct about the types of possible sequences. However, one student made a computational error because it is not possible to arrive at a fourth term of 44 in two different ways.

• Both students could be correct. Because two numbers are given in the original sequence, it is possible to find a common difference and common ratio between the successive terms.

A sequence is defined by the recursive formula

f(n + 1) = 1.5f(n)

Which sequence could be generated using the formula?

• –20, 30, –45, ...

• –12, –18, –27, ...

• –18, –16.5, –15, ...

• –16, –17.5, –19, ...

What ordered pair is closest to a local minimum of the function, f(x)?

• (–1, –3)

• (0, –2)

• (1, 4)

• (2, 1)

Which is a valid prediction about the continuous function f(x)?

• f(x) ≤ 0 over the interval (–∞, ∞).

• f(x) > 0 over the interval (–1, ∞).

• f(x) ≥ 0 over the interval [–1, 1].

What are the x-intercepts of the graphed function?

• (–3, 0) and (0, 1.5)

• (0, 1.5) and (1, 0)

• (–3, 0) and (1,0)

What is x when f(x)=0?

• -1.2

• 0

• -1.8

• 5

What is f(0)?

• 4

• 5

• 6

• 7

What is the domain of the given function?

• {x | x = –6, –1, 0, 3}

• {y | y = –7, –2, 1, 9}

• {x | x = –7, –6, –2, –1, 0, 1, 3, 9}

• {y | y = –7, –6, –2, –1, 0, 1, 3, 9}

What is the range of the function on the graph?

• all the real numbers

• all the real numbers greater than or equal to 0

• all the real numbers greater than or equal to 2

• all the real numbers greater than or equal to –3