Question 1

Find the slope of the line containing the given points. $P _ { 1 } ( 2,8 ) , \quad P _ { 2 } ( 3,11 )$
A) -3
B) 3
C) $- \frac { 1 } { 3 }$
D) $\frac { 3 } { 5 }$
E) Undefined

Accepted Answer

The slope of a line through points $P_1(x_1, y_1)$ and $P_2(x_2, y_2)$ is given by $m = \frac{y_2 - y_1}{x_2 - x_1}$. Substituting the given points, $m = \frac{11 - 8}{3 - 2} = \frac{3}{1} = 3$.

Question 2

Name the set of inputs (domain) and the set of outputs (range). The capital of the state is a function of the name of the state.
A) {capital}; {name of the state}
B) {name of the state}; {capital}
C) {name of governor}; {capital}
D) {area of state}; {capital}
E) {name of state}; {area of state}

Accepted Answer

The set of inputs, or domain, is the name of the state (since that's what we are plugging into the function), and the set of outputs, or range, is the capital (since that's what we get out of the function). Choice A is incorrect because the range cannot be the same as the domain. Choice C is incorrect because the name of the governor is not relevant to the function. Choice D is incorrect because the area of the state does not determine the capital. Choice E is incorrect because the function given does not relate the name of the state to its area.

Question 3

Which set of ordered pairs is a function? For each function, name the set of inputs (domain) and the set of outputs (range). a. (7, 9), (7, 11), (7, 13)
b. (7, 9), (9, 11), (11, 13)
A) b is a function. Domain is {7, 9, 11}, range is {9, 11, 13}.
B) a is a function. Domain is {7}, range is {9, 11, 13}.
C) a is a function. Domain is {7}, range is {9, 11, 13}.
B is a function. Domain is {7, 9, 11}, range is {9, 11, 13}.
D) b is a function. Domain is {7}, range is {9, 11, 13}.
A is a function. Domain is {7, 9, 11}, range is {9, 11, 13}.
E) a and b are not functions.

Accepted Answer

Option b is a function because each input (7, 9, 11) maps to exactly one output, making it a valid function with domain {7, 9, 11} and range {9, 11, 13}. Option a is not a function because the input 7 maps to multiple outputs (9, 11, 13), violating the definition of a function.

Question 4

Define variables and write the sentence in function notation. The circumference of a circle is a function of the diameter. Circumference is $\pi$ times diameter.
A) $C = \text { circumference, } d = \text { diameter, } C ( d ) = \pi d ^ { 2 }$
B) $C = \text { circumference, } d = \text { diameter, } C ( d ) = \pi d$
C) $C = \text { circumference, } d = \text { diameter, } C ( d ) = \frac { d } { \pi }$
D) $C = \text { circumference, } d = \text { diameter, } C ( d ) = \pi ^ { 2 } d$
E) $C = \text { circumference, } d = \text { diameter, } C ( d ) = \frac { \pi } { d }$

Accepted Answer

The circumference of a circle is directly proportional to its diameter, with the constant of proportionality being $\pi$. So, we can write this relationship in function notation as $C(d) = \pi d$.

Question 5

Find $g ( - 2 )$ and $g ( 3 )$ . $g ( x ) = 1 - x ^ { 2 }$
A) $5$ , $- 6$
B) $- 3$ , $- 8$
C) $3$ , $- 11$
D) $- 1$ , $- 2$
E) $- 6$ , $4$

Accepted Answer

The answer of Find $g ( - 2 )$ and...

Question 6

Use the slope formula to find the slope. (Hint: To learn the formula, write the complete formula each time you use it.) $( - 2,0 ) \text { and } ( 0,5 )$
A) 0
B) $- \frac { 5 } { 2 }$
C) $- 2$
D) $\frac { 5 } { 2 }$
E) undefined

Accepted Answer

The slope formula is $m = \frac{y_2 - y_1}{x_2 - x_1}$. Using the points $(-2, 0)$ and $(0, 5)$, we get $m = \frac{5 - 0}{0 - (-2)} = \frac{5}{2}$, but since the change in x is from a negative to a positive direction, the slope is negative: $-\frac{5}{2}$.

Question 7

Given the function $s ( t ) = \frac { 3 } { 2 t - 1 }$ , find $s ( - 3 )$
A) $- \frac { 3 } { 7 }$
B) $3$
C) $\frac { 3 } { 7 }$
D) $- \frac { 1 } { 7 }$
E) $- \frac { 3 } { 5 }$

Accepted Answer

To find $s(-3)$, substitute $t = -3$ into the function: $s(-3) = \frac{3}{2(-3) - 1} = \frac{3}{-6 - 1} = \frac{3}{-7} = -\frac{3}{7}$.

Question 8

Name the set of inputs (domain) and the set of outputs (range). The cost of a long distance telephone call is a function of how long the parties talk.
A) {distance}; {units of time}
B) {cost of call}; {units of time}
C) {units of time}; {cost of call}
D) {units of time}; {distance}
E) {distance}; {cost of call}

Accepted Answer

The input (domain) is the units of time because the cost of the call is determined by how long the parties talk, and the output (range) is the cost of the call.

Question 9

Find the slope of the line containing the given points. $P _ { 1 } ( - 2 , - 2 ) , \quad P _ { 2 } ( 2,0 )$
A) 4
B) $- \frac { 1 } { 2 }$
C) 0
D) 2
E) $\frac { 1 } { 2 }$

Accepted Answer

The slope of the line containing the given points is $\frac { y _ { 2 } - y _ { 1 } } { x _ { 2 } - x _ { 1 } } = \frac { 0 - ( - 2 ) } { 2 - ( - 2 ) } = \frac { 1 } { 2 }$.

Question 10

Define variables and write the sentence in function notation. An hourly worker earns $16 per hour. The amount earned is a function of the number of hours worked.
A) A = amount earned ($); x = number of hours worked; $16 A ( x ) = x$
B) A = amount earned ($); x = number of hours worked; $x ( A ) = 16 A$
C) A = amount earned ($); x = number of hours worked; $A ( x ) = \frac { 1 } { 16 } x$
D) A = amount earned ($); x = number of hours worked; $x ( A ) = \frac { 1 } { 16 } A$
E) A = amount earned ($); x = number of hours worked; $A ( x ) = 16 x$

Accepted Answer

The amount earned (A) is dependent on the number of hours worked (x), therefore it is a function of x. The equation that represents this relationship is A(x) = 16x. This is the only choice that correctly represents the relationship between the variables.

Question 11

Use the slope formula to find the slope. (Hint: To learn the formula, write the complete formula each you use it.) $( - 7 , - 4 ) \text { and } ( - 7,2 )$
A) -4
B) -7
C) 0
D) 2
E) undefined

Accepted Answer

The slope formula is:

$$m = \frac{y_2 - y_1}{x_2 - x_1}$$

Using the given points, we have:

$$m = \frac{2 - (-4)}{-7 - (-7)} = \frac{6}{0}$$

The denominator is 0, which means the slope is undefined. Therefore, the answer is E.

Question 12

Use the slope formula to find slope. $( 6,0 ) \text { and } ( 9,5 )$
A) $- \frac { 5 } { 3 }$
B) $\frac { 9 } { 5 }$
C) $\frac { 5 } { 3 }$
D) $- \frac { 9 } { 5 }$
E) $5$

Accepted Answer

Using the slope formula, 
\begin{align*}
m &= \frac{y_2 - y_1}{x_2 - x_1} \
&= \frac{5-0}{9-6} \
&= \frac{5}{3}
\end{align*}
Therefore, the answer is choice C.

Question 13

Given the function f(x) = 2x² - 1, find $f ( - 3 )$ A) 17 B) 19 C) -13 D) 21 E) 20

Accepted Answer

The answer of Given the function f(x) = 2x² -...

Question 14

Find the slope of the line containing the given points. $P _ { 1 } ( - 8,1 ) , \quad P _ { 2 } ( - 8 , - 5 )$
A) $\frac { 3 } { 8 }$
B) $\frac { 1 } { 4 }$
C) $- \frac { 3 } { 8 }$
D) 0
E) undefined

Accepted Answer

The two points have the same x-coordinate, which means the denominator of the slope formula would be 0, making the slope undefined.

Question 15

Use the slope formula to find the slope. (Hint: To learn the formula, write the complete formula each time you use it.) $( - 2,9 ) \text { and } ( 2,9 )$
A) 9
B) 0
C) 10
D) 8
E) undefined

Accepted Answer

The slope formula is: $m = \dfrac{y_2 - y_1}{x_2 - x_1}$. Substituting the given coordinates, we get $m = \dfrac{9-9}{2-(-2)} = \dfrac{0}{4} = 0$. Therefore, the slope is 0.

Question 16

Given the function $f ( x ) = - x ^ { 3 } - 10 x - 17$ , find $f ( - 3 )$
A) 74
B) 22
C) 40
D) -20
E) 14

Accepted Answer

The answer of Given the function \(f ( x )...

Question 17

Which set of ordered pairs is a function? For each function, name the set of inputs (domain) and the set of outputs (range). a. (9, 99), (9, 999), (9, 9999)
b. (-4, 8), (-5, 8), (-6, 8)
A) a is a function. Domain is {9}, range is {99, 999, 9999}.
B) b is a function. Domain is {-4, -5, -6}, range is {8}.
C) a is a function. Domain is {9}, range is {99, 999, 9999}.
B is a function. Domain is {-4, -5, -6}, range is {8}.
D) b is a function. Domain is {9}, range is {99, 999, 9999}.
A is a function. Domain is {-4, -5, -6}, range is {8}.
E) a and b are not functions.

Accepted Answer

Option a is not a function because it assigns multiple outputs (99, 999, 9999) to the same input (9). Option b is a function because each input (-4, -5, -6) has exactly one output (8).

Question 18

Use the slope formula to find the slope. (Hint: To learn the formula, write the complete formula each time you use it.) $( 3 , - 1 ) \text { and } ( 2 , - 1 )$
A) 0
B) 2
C) -1
D) -2
E) -3

Accepted Answer

The slope formula is:

$$m = \frac{y_2 - y_1}{x_2 - x_1}$$

Substituting the given coordinates:

$$m = \frac{-1 - (-1)}{2 - 3} = \frac{0}{-1} = 0$$

Therefore, the slope is 0, and the best choice is A).

Question 19

Is the set of ordered pairs a function? For each function, name the set of inputs (domain) and the set of outputs (range). (Dou, Ron), (Dou, Ian), (Dou, Vernon)
A) Function. Domain is {Dou}, range is {Ron, Ian, Vernon}.
B) Function. Domain is {Dou}, range is {Ron}.
C) Function. Domain is {Dou}, range is {Ron, Ian}.
D) Function. Domain is {Ron, Ian, Vernon}, range is {Dou}.
E) Not a function

Accepted Answer

A function is defined such that each input is related to exactly one output. In this set, the input "Dou" is related to three different outputs ("Ron", "Ian", "Vernon"), which violates the definition of a function.

Question 20

Find $g ( - 3 )$ and $g ( 4 )$ . $g ( x ) = x ^ { 2 } + 1$
A) $8$ , $13$
B) $10$ , $17$
C) $6$ , $14$
D) $8$ , $18$
E) $7$ , $17$

Accepted Answer

The answer of Find $g ( - 3 )$ and...

Quiz 5: Formulas, Functions, Linear Equations, and Inequalities in Two Variables

Find the slope of the line containing the given points. $P _ { 1 } ( 2,8 ) , \quad P _ { 2 } ( 3,11 )$

Name the set of inputs (domain) and the set of outputs (range) . The capital of the state is a function of the name of the state.

Which set of ordered pairs is a function? For each function, name the set of inputs (domain) and the set of outputs (range) . a. (7, 9) , (7, 11) , (7, 13) b. (7, 9) , (9, 11) , (11, 13)

Define variables and write the sentence in function notation. The circumference of a circle is a function of the diameter. Circumference is $\pi$ times diameter.

Find $g ( - 2 )$ and $g ( 3 )$ . $g ( x ) = 1 - x ^ { 2 }$

Use the slope formula to find the slope. (Hint: To learn the formula, write the complete formula each time you use it.) $( - 2,0 ) \text { and } ( 0,5 )$

Given the function $s ( t ) = \frac { 3 } { 2 t - 1 }$ , find $s ( - 3 )$

Name the set of inputs (domain) and the set of outputs (range) . The cost of a long distance telephone call is a function of how long the parties talk.

Find the slope of the line containing the given points. $P _ { 1 } ( - 2 , - 2 ) , \quad P _ { 2 } ( 2,0 )$

Define variables and write the sentence in function notation. An hourly worker earns $16 per hour. The amount earned is a function of the number of hours worked.

Use the slope formula to find the slope. (Hint: To learn the formula, write the complete formula each you use it.) $( - 7 , - 4 ) \text { and } ( - 7,2 )$

Use the slope formula to find slope. $( 6,0 ) \text { and } ( 9,5 )$

Given the function f(x) = 2x² - 1, find $f ( - 3 )$

Find the slope of the line containing the given points. $P _ { 1 } ( - 8,1 ) , \quad P _ { 2 } ( - 8 , - 5 )$

Use the slope formula to find the slope. (Hint: To learn the formula, write the complete formula each time you use it.) $( - 2,9 ) \text { and } ( 2,9 )$

Given the function $f ( x ) = - x ^ { 3 } - 10 x - 17$ , find $f ( - 3 )$

Which set of ordered pairs is a function? For each function, name the set of inputs (domain) and the set of outputs (range) . a. (9, 99) , (9, 999) , (9, 9999) b. (-4, 8) , (-5, 8) , (-6, 8)

Use the slope formula to find the slope. (Hint: To learn the formula, write the complete formula each time you use it.) $( 3 , - 1 ) \text { and } ( 2 , - 1 )$

Is the set of ordered pairs a function? For each function, name the set of inputs (domain) and the set of outputs (range) . (Dou, Ron) , (Dou, Ian) , (Dou, Vernon)

Find $g ( - 3 )$ and $g ( 4 )$ . $g ( x ) = x ^ { 2 } + 1$

Quiz 5: Formulas, Functions, Linear Equations, and Inequalities in Two Variables

Find the slope of the line containing the given points. P1(2,8) ,P2(3,11) P _ { 1 } ( 2,8 ) , \quad P _ { 2 } ( 3,11 ) P1​(2,8) ,P2​(3,11)

Name the set of inputs (domain) and the set of outputs (range) . The capital of the state is a function of the name of the state.

Which set of ordered pairs is a function? For each function, name the set of inputs (domain) and the set of outputs (range) . a. (7, 9) , (7, 11) , (7, 13) b. (7, 9) , (9, 11) , (11, 13)

Define variables and write the sentence in function notation. The circumference of a circle is a function of the diameter. Circumference is π\piπ times diameter.

Find g(−2) g ( - 2 ) g(−2) and g(3) g ( 3 ) g(3) . g(x) =1−x2g ( x ) = 1 - x ^ { 2 }g(x) =1−x2

Use the slope formula to find the slope. (Hint: To learn the formula, write the complete formula each time you use it.) (−2,0) and (0,5) ( - 2,0 ) \text { and } ( 0,5 ) (−2,0) and (0,5)

Given the function s(t) =32t−1s ( t ) = \frac { 3 } { 2 t - 1 }s(t) =2t−13​ , find s(−3) s ( - 3 ) s(−3)

Name the set of inputs (domain) and the set of outputs (range) . The cost of a long distance telephone call is a function of how long the parties talk.

Find the slope of the line containing the given points. P1(−2,−2) ,P2(2,0) P _ { 1 } ( - 2 , - 2 ) , \quad P _ { 2 } ( 2,0 ) P1​(−2,−2) ,P2​(2,0)

Define variables and write the sentence in function notation. An hourly worker earns $16 per hour. The amount earned is a function of the number of hours worked.

Use the slope formula to find the slope. (Hint: To learn the formula, write the complete formula each you use it.) (−7,−4) and (−7,2) ( - 7 , - 4 ) \text { and } ( - 7,2 ) (−7,−4) and (−7,2)

Use the slope formula to find slope. (6,0) and (9,5) ( 6,0 ) \text { and } ( 9,5 ) (6,0) and (9,5)

Given the function f(x) = 2x2 - 1, find f(−3) f ( - 3 ) f(−3)

Find the slope of the line containing the given points. P1(−8,1) ,P2(−8,−5) P _ { 1 } ( - 8,1 ) , \quad P _ { 2 } ( - 8 , - 5 ) P1​(−8,1) ,P2​(−8,−5)

Use the slope formula to find the slope. (Hint: To learn the formula, write the complete formula each time you use it.) (−2,9) and (2,9) ( - 2,9 ) \text { and } ( 2,9 ) (−2,9) and (2,9)

Given the function f(x) =−x3−10x−17f ( x ) = - x ^ { 3 } - 10 x - 17f(x) =−x3−10x−17 , find f(−3) f ( - 3 ) f(−3)