Answers 25-26 MATH 1 - S1Recognizing Patterns

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On a coordinate plane, a curved line crosses the y-axis at (0, 1), crosses the x-axis at (.25, 0), turns at point (2, negative 3), and crosses the x-axis (3.75, 0).

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

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Which set of ordered pairs represents a function?

{(2, –2), (1, 5), (–2, 2), (1, –3), (8, –1)}

{(3, –1), (7, 1), (–6, –1), (9, 1), (2, –1)}

{(6, 8), (5, 2), (–2, –5), (1, –3), (–2, 9)}

{(–3, 1), (6, 3), (–3, 2), (–3, –3), (1, –1)}

What is the inverse of the function f(x) = x – 12?

h(x) = 48x – 4

h(x) = 48x + 4

h(x) = 4x – 48

h(x) = 4x + 48

The table represents the function f(x).

–29

–10

–3

–1

The graph of the function f(x) is shown below.

-1.8

-1.2

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 –2.

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.

For one month Siera calculated her home town’s average high temperature in degrees Fahrenheit. She wants to convert that temperature from degrees Fahrenheit to degrees Celsius using the function . What does C(F) represent?

C(F) represents the output of the function C in degrees Celsius when the input F is in degrees Fahrenheit

C(F) represents the output of the function F in degrees Fahrenheit when the input C is in degrees Celsius

C(F) represents the output of the function C in degrees Fahrenheit when the input F is in degrees Celsius

C(F) represents the output of the function F in degrees Celsius when the input C is in degrees Fahrenheit

Consider the function represented by the table.

A sequence is defined by the recursive formula f(n + 1) = 1.5f(n). Which sequence could be generated using the formula?

–12, –18, –27, ...

–20, 30, –45, ...

–18, –16.5, –15, ...

–16, –17.5, –19, ...

A 2-column table with 7 rows. The first column is labeled x with entries negative 6, negative 4, negative 2, 0, 2, 4, 6. The second column is labeled f of x with entries 8, 2, 0, negative 2, negative 1, 0, 4.

(–2, 0)

(0, –2)

(2, –1)

(4, 0)

A 2-column table with 6 rows. The first column is labeled x with entries negative 3, negative 2, negative 1, 0, 1. The second column is labeled f of x with entries 15, negative 5, 0, 5, 0, negative 5.

f(x) ≤ 0 over the interval (–∞, ∞).

f(x) > 0 over the interval (–1, ∞).

f(x) ≥ 0 over the interval [–1, 1].

f(x) < 0 over the interval (0, 2).

Which statements about the local maximums and minimums for the given function are true? Choose three options.

Over the interval [1, 3], the local minimum is 0

Over the interval [2, 4], the local minimum is –8.

Over the interval [3, 5], the local minimum is –8.

Over the interval [1, 4], the local maximum is 0.

Over the interval [3, 5], the local maximum is 0.

A 2-column table with 6 rows. The first column is labeled x with entries negative 2, negative 1, 0, 1, 2, 3. The second column is labeled f of x with entries negative 8, negative 3, negative 3, 4, 1, 3.

(–1, –3)

(0, –2)

(1, 4)

(2, 1)

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.

A 2-column table with 6 rows. The first column is labeled x with entries negative 4, negative 2, 0, 2, 4, 6. The second column is labeled f of x with entries 0, 2, 8, 2, 0, negative 2.

(0, 8)

(–4, 0)

(–4, 0), (4, 0)

(–4, 0), (0, 8), (4, 0)

The table represents a function.

–6

–2

On a coordinate plane, a curved line with a minimum value of (0, 1) and a maximum value of (negative 1.3, 2.2), crosses the x-axis at (negative 2.2, 0) and crosses the y-axis at (0, 1).

Over the interval [–3, –2], the local minimum is 0.

Over the interval [–2, –1], the local minimum is 2.2.

Over the interval [–1, 0.5], the local minimum is 1.

Over the interval [0.5, 2], the local minimum is 4.

The graph represents a functional relationship.

–14

–2

The volume of air inside a rubber ball with radius r can be found using the function . What does represent?

the radius of the rubber ball when the volume equals cubic feet

the volume of the rubber ball when the radius equals feet

that the volume of the rubber ball is 5 cubic feet when the radius is 7 feet

that the volume of the rubber ball is 7 cubic feet when the radius is 5 feet

The function h(t) = –16t2 + 28t + 500 represents the height of a rock t seconds after it is propelled by a slingshot.

the height of the rock 3.2 seconds before it reaches the ground

the time it takes the rock to reach the ground, or 3.2 seconds

the time it takes the rock to reach a height of 3.2 meters

the height of the rock 3.2 seconds after it is propelled

On a coordinate plane, a curved line with a maximum value of (negative 1, 2) crosses the x-axis at (negative 3, 0) and (1, 0), and crosses the y-axis at (0, 1.5).

(–3, 0) and (0, 1.5)

(–3, 0) and (1,0)

(–1, 2) and (1, 0)

(0, 1.5) and (1, 0)

A 2-column table with 4 rows. The first column is labeled x with entries negative 6, negative 1, 0, 3. The second column is labeled y with entries negative 7, 1, 9, negative 2.

{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}

The function f(x) is shown on the graph.

12 only

2 and 3 only

–2, –1, 1, and 2 only

–2, –1, 1, 2 and 12

Which recursive formula can be used to generate the sequence shown, where f(1) = 9.6 and n > 1?9.6, –4.8, 2.4, –1.2, 0.6, ...

f(n + 1) = (–0.5)f(n)

f(n + 1) = (0.5)f(n)

f(n + 1) = f(0.5n)

f(n + 1) = f(–0.5n)

Which graph shows a set of ordered pairs that represent a function?

Option

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