algebra 1b - unit 1: exploring functions

a sequence has an initial term a1 = 22 and a recursive formula an = an−1 − 10. what is the explicit formula for the sequence?

an = 22 − 10(n − 1)

which explicit formula represents the sequence?

an = −2 + 5(n − 1)

which of the following shows a line test correctly used to show that leah's equation does not define a function of x?

https://cdstools.flipswitch.com/asset/media/1008400

which of the following maps represent functions?

https://cdstools.flipswitch.com/asset/media/1155188 https://cdstools.flipswitch.com/asset/media/1155190 https://cdstools.flipswitch.com/asset/media/1155189

which of the following images are graphs of functions?

https://cdstools.flipswitch.com/asset/media/1155195 https://cdstools.flipswitch.com/asset/media/1155194 https://cdstools.flipswitch.com/asset/media/1155196

which of the following graphs represent functions?

https://cdstools.flipswitch.com/asset/media/1155200 https://cdstools.flipswitch.com/asset/media/1155199

which of the mapping diagrams represents a function?

https://cdstools.flipswitch.com/asset/media/1155204

examine the following graphs and determine which relations are functions. select all that apply.

https://cdstools.flipswitch.com/asset/media/1155209 https://cdstools.flipswitch.com/asset/media/1155208

lesson 1

introduction to functions

which statement correctly describes the range of a function?

it is all of the possible output values of a function.

which situation can be modeled by a function?

natalie can spend $15 on 1 shirt, $30 on 2 shirts, or $45 on 3 shirts.

examine the following graph. https://cdstools.flipswitch.com/asset/media/1009274 does the graph represent a function? why or why not?

no, because the graph fails the vertical line test.

the following list of ordered pairs maps animals to foods. is the relation a function? why or why not?

no, there is an input that has more than one output.

the following mapping diagram maps names to methods of transportation. https://cdstools.flipswitch.com/asset/media/1155187 is the relation a function? why or why not?

no, there is an input that maps to more than one output.

jovanna has a job where she earns $10.75 per hour and earns a $40 weekly bonus if she provides excellent customer service. assuming jovanna always provides excellent customer service, which function, p(h), where h is the number of hours jovanna worked, represents her weekly paycheck?

p(h) = 10.75h + 40

a ride sharing service charges $4.25 for every ride, plus $0.30 per mile. if m represents miles, which rule for p(m) models the situation?

p(m) = 0.30m + 4.25

lesson 2

properties of functions

the following graph represents a function. https://cdstools.flipswitch.com/asset/media/1155374 what are the domain and range of the function?

range: {0, 2, −4, −8} domain: {−2, −1, 0, 1, 2}

what are the domain and range of the function?

range: {−2, 0, 1, 2, 3} domain: {−4, −2, 0, 2, 4}

a sequence begins with −3. each term is calculated by multiplying the previous term by −4, then subtracting 1. which option correctly represents the sequence described?

{−3, 11, −45, 179, ...}

look at the graph of connected points in the plane which make up a function. https://cdstools.flipswitch.com/asset/media/1009297 what is the range of the function?

−2 ≤ f(x) ≤ 4

which two solutions to the equation x^2 + y^2 = 20 can be used to show that it is not a function?

(4, 2) (4, -2)

which two ordered pairs generated by x = y^2 − 1 can be used to show that the equation is not a function?

(8, 3) and (8, −3)

the following table shows a relation. x: -2, -1, 3, 9 y: -1, 9, 17, 22 which numbers are part of the relation's output? select all that apply.

-1, 9, 17, 22

the explicit formula for a sequence is an = 12 - 5(n - 1) what is the 30th term of the sequence?

-133

what is the common difference between the terms in the following sequence? {17, 11, 5, −1, −7 ...}

-6

in the arithmetic sequence {13, 6, −1, −8,...}, what is the common difference?

-7

what is the output of f when x = −6?

1.2

the explicit formula for a sequence is an = -1 + 3(n - 1) what is the 55th term of the sequence?

161

the explicit formula for a sequence is an = -2 + 3/2(n - 1) what is the 21st term of the sequence?

28

the following function represents an arithmetic sequence. f(1) = −1.5 f(n + 1) = f(n) + 0.5 what is f(10)?

3

use the recursive formula to answer the question. a1 = 12 an = an-1 + 4 what is the 7th term in the sequence?

36

the following function represents an arithmetic sequence. f(1) = 2 f(n+1) = f(n) + 4 what is f(10)?

38

the function f(n) represents an arithmetic sequence where the first term is 5 and each term increases by 5. what is f(8)?

40

in the arithmetic sequence {−9, −4, 1, 6, 11, ...}, what is the common difference?

5

use the recursive formula to answer the question. a1 = 20 an = an-1 - 5 what is the 4th term in the sequence?

5

use the following recursive formula to answer the question. a1 = -3/2 an = an-1 + 1/2 what is a9?

5/2

which of the following statements is true?

a function, f, assigns each element of the domain to one element in the range.

use the given terms of the sequence to answer the question. a1 = 10 a2 = 6 a3 = 2 a4 = -2 which recursive formula represents the sequence?

a1 = 10 an = an-1 - 4

the first term in a sequence is 9. each value in the sequence is 4 more than the previous value. what is the recursive formula for this sequence?

a1 = 9 and an = an−1 + 4

a sequence has the explicit formula an = −4 + 7(n − 1). what is the recursive formula for the sequence?

a1 = −4a an = an−1 + 7

which statement describes the domain of a function?

all of the possible input values for which a function is defined

examine the following graph. https://cdstools.flipswitch.com/asset/media/1155222 what is the domain of the function represented by the graph?

all real numbers

examine the following graph. https://cdstools.flipswitch.com/asset/media/1155223 what is the range of the function represented by the graph?

all real numbers

what is the domain of the equation y = 2/5x − 4?

all real numbers

what is the domain of the function f(x) = −1/2x + 15?

all real numbers

what is the range of f(x) if f(x) = x^2?

all real numbers greater than or equal to 0

what is the recursive formula for the sequence {−4, −1, 2, 5, ...}?

f(1) = −4 and f(n + 1) = f(n) + 3

what is the value of f(3) for the function f(x) = 4x − 1?

f(3) = 11

examine the following graph. https://cdstools.flipswitch.com/asset/media/1155244 what is the explicit formula represented by this graph?

f(n) = 1 − 3(n − 1)

which function correctly represents the arithmetic sequence {20, 23, 26, 29, 32}?

f(n) = 3n + 17

wich of the following functions represents an arithmetic sequence?

f(n) = 3n − 4

which function rule defines f(x)?

f(x) = -2x - 5

gabriel earns $11.25 per hour at his job. he also receives a bonus of $20 each week if he arrives on time for each of his shifts. assuming gabriel is always on time, and x is the number of hours he works, which rule for f(x) models his weekly paycheck?

f(x) = 11.25x + 20

which answers are written in function notation? select all that apply.

f(x) = 2x − 4 p(n) = n^2 − 2n + 1

given a function, f, f(x) is in the domain of the function. is the previous statement true or false?

false

lesson 5

formulas of sequences

a function, named g, has an input of c and a range of all real numbers. which option best represents the described function?

g(c) = 4/5c + 2/5

which of the following answers is written in function notation and has a range of all real numbers?

g(x) = 1/2x + 3/2

which function rule defines g(x)?

g(x) = 1/3x + 7

which function rule represents the input-output table?

h(x) = 3x + 5

which function rule defines the values given in the list of ordered pairs?

h(x) = 9x - 1

let g be a function. which statements are true for all functions g? select all that apply.

the value of g(a) is the output of gg corresponding to the input a. the function g assigns each element of the domain exactly one element of the range.

lesson 4

sequences

which is the correct way to evaluate ff(15) for the function f(x) = 2(x + 3)?

start by substituting 15 for x. then, simplify to get f(15) = 36.

use the following sequence to answer the question. {4, −5, 13, −23,...} which answer correctly describes the sequence?

start with 4, then calculate each term by multiplying the previous term by −2, and then adding 3.

the following graph represents a function. https://cdstools.flipswitch.com/asset/media/1155203 which reasons prove that the graph represents a function? select all that apply.

the graph passes the vertical line test. there is exactly one output for each input.

joe bought an apple tree that was 48 inches in height. he noticed that this tree grew approximately 4 inches in height each year. which statement best describes the function that could be used to model the height of the apple tree, h(t), as a function of time, t, in years.

the height of the apple tree can be represented by a linear function, and the variable t is multiplied by 4 in the equation representing the function.

which answer describes the sequence {1, 3, 7, 15, ...} as a mathematical statement?

the nth value equals 1 more than twice the previous value.

which statement correctly describes the graphed function f(x) = −x + 5, with a domain restricted to natural numbers, in terms of an arithmetic sequence?

the point (1, 4) means the 1st1st term of the sequence is 4. the point (2, 3) means the 2nd2nd term of the sequence is 3, and so on.

which sequence represents the function f(x) = 7x − 4, with a domain of natural numbers?

{3, 10, 17, 24, ...}

which sequence is an arithmetic sequence?

{−10, −3.5, 3, 9.5, ...}

a sequence begins with −15. each term is calculated by adding 6 to the previous term. which answer correctly represents the sequence described?

{−15, −9, −3, 3,...}

lesson 3

working with functions

use the graph of the quadratic function to answer the question. https://cdstools.flipswitch.com/asset/media/1077576 which statement describes the domain of the function?

x can be any real number.

consider the quadratic function f(x) = −x^2 − 6x − 4, which has been given a restricted domain, as shown in the following graph. what is the domain of f(x)?

x ≤ −1

the following tables represent relations. which of the tables also represent a function? select all that apply.

x: -2, -1, 0, 1, 2 y: 4, 1, 0, 1, 4 x: -1, 1, 3, 4, 5 y: 3, 3, 3, 3, 3 x: -2, -1, 0, 1, 2 y: 4, 2, 0.5, 1, 1.5

which is the correct input-output table for the function g(x) = −1/2(4x + 6)?

x: -2, 0, 2, 4 f(x): 1, -3, -7, -11

look at the equation below. y = 3x^2 which of these tables represents solutions for this equation?

x: -4, -2, 1, 5 y: 48, 12, 3, 75

which is the correct input-output table for the function f(x) = x^2 + 2x + 1?

x: 0, 1, 2, 3 f(x): 1, 4, 9, 16

which is the correct input-output table for the function f(x) = 3x^2 − x + 4?

x: 0, 1, 2, 3 f(x): 4, 6, 14, 28

which of the following tables represents y as a function of x?

x: 5, 2, 6, 4, 1, 3 y: 2, 2, 2, 2, 2, 2

use the graph of the quadratic function to answer the question https://cdstools.flipswitch.com/asset/media/1077580 which statement correctly describes the range of the function?

y ≥ −8

the following table represents a relation. does the table represent y as a function of x? why or why not?

yes, because there are no x-values with more than one y-value.

which of the following relations is also a function?

{(1, 1), (3, 2), (6, 3), (8, 4)}

which of the following sets of ordered pairs does not define a function?

{(1, 3), (5, 2), (6, 9), (1, 12), (10, 2)}

which sequence represents the function f(x) = x − 3, with a domain of natural numbers?

{-2, -1, 0, 1, ....}

the following relation maps x-values to y-values. x: 0, 2, 4, 6 y: 0, 1, 2, 3 what is the set of input values?

{0, 2, 4, 6}

which of the following sequences is an arithmetic sequence?

{1, 4, 7, 10, ...}

a sequence begins with 2. each term is calculated by multiplying the previous term by −1, then subtracting 3. which answer correctly represents the sequence described?

{2, −5, 2, −5,...}