Question 1

Find the domain of  
A) 
B) 
C) 
D) 
E)

Accepted Answer

B

Question 2

Find the midpoint of the segment AB between the points A (- 3, - 5) and B (15, 7)
A)( 6, 1 )
B)( 15, 1 )
C)( 3, 1 )
D)( 1, 1 )
E)( 6, 7 )

Accepted Answer

The midpoint of a segment with endpoints $A(x_1, y_1)$ and $B(x_2, y_2)$ is given by $\left(\frac{x_1 + x_2}{2}, \frac{y_1 + y_2}{2}\right)$. Substituting $A(-3, -5)$ and $B(15, 7)$ gives $\left(\frac{-3 + 15}{2}, \frac{-5 + 7}{2}\right) = (6, 1)$.

Question 3

Let y = f (x) be a function with domain D = [ -6, -3 ] and range R = [ -8, -2 ]. Find the domain D and range R for the function 
A) 
B) 
C) 
D) 
E)

Accepted Answer

C

Question 4

A cable television firm presently serves 5,900 households and charges $22 per month. A marketing survey indicates that each decrease of $1 in the monthly charge will result in 590 new customers. Let R(x) denote the total monthly revenue when the monthly charge is x dollars. Find the value of x that results in maximum monthly revenue.
A)$21
B)$6
C)$11
D)$16
E)$22

Accepted Answer

The answer of A cable television firm presently serves 5,900...

Question 5

Find the domain of  
A) 
B) 
C) 
D) 
E)

Accepted Answer

The answer of Find the domain of  
A) 
B)...

Question 6

Express the function in the form of  . 
A) 
B) 
C) 
D) 
E)

Accepted Answer

The answer of Express the function in the form of...

Question 7

Express the function  in the form of  
A) 
B) 
C) 
D) 
E)

Accepted Answer

The answer of Express the function  in the form...

Question 8

The owner of an ice cream franchise must pay the parent company $1,100 per month plus 5% of the monthly revenue R. Operating cost of the franchise includes a fixed cost of $2,500 per month for items such as utilities and labor. The cost of ice cream and supplies is 50% of the revenue. Determine the monthly revenue needed to break even.
A)$3,600
B)$1,620
C)$1,400
D)$8,000
E)$6,545

Accepted Answer

To break even, the total cost must equal the total revenue. The total cost includes the fixed franchise fee, the fixed operating cost, and the variable cost of ice cream and supplies. The total cost equation is: $1,100 + 0.05R + $2,500 + 0.5R. The revenue is simply R. Setting the total cost equal to the revenue gives us the equation: $1,100 + $2,500 + 0.05R + 0.5R = R. Simplifying, we get $3,600 + 0.55R = R, which leads to 0.45R = $3,600. Solving for R gives R = $8,000.

Question 9

If are real numbers, find A)f ( a ) + f ( h ) = a² + h² + a + h + 6 B)f ( a ) + f ( h ) = a² + h² - a - h + 6 C)f ( a ) + f ( h ) = a² + h² - a - h D)f ( a ) + f ( h ) = a² + h² - a - h - 6 E)f ( a ) + f ( h ) = a² + h² + a + h

Accepted Answer

The answer of If  are real numbers, find ...

Question 10

Given the two lines graphed on the same coordinate plane, find the coordinates of the point of intersection (the coordinates are integers).  
A)( - 17, 11 )
B)( - 11, 14 )
C)( - 11, 12 )
D)( - 16, 12 )
E)( - 11, 17 )

Accepted Answer

The answer of Given the two lines graphed on the...

Question 11

Consider the following equations and their graph. Express, in interval form, the x-values such that Y₁ > Y₂ . Assume that the x- and y-values of each point of intersection are integers. A) B) C) D) E)

Accepted Answer

The answer of Consider the following equations and their graph....

Question 12

Find the point with coordinates of the form (2a, a) that is in the third quadrant and is a distance 9 from P(3, 4).
A)( - 3.90, - 1.95 )
B)( - 4.00, - 1.90 )
C)( - 3.70, - 1.85 )
D)( - 4.00, - 7.99 )
E)( - 3.80, - 1.90 )

Accepted Answer

The answer of Find the point with coordinates of the...

Question 13

Use tests for symmetry to determine if the graph of the function is symmetric with respect to the y-axis, the x-axis, or the origin. 
A)the graph is symmetric with respect to the x-axis
B)the graph is symmetric with respect to the y-axis
C)the graph is symmetric with respect to the x-axis and the y-axis
D)the graph is symmetric with respect to the origin
E)the graph is not symmetric

Accepted Answer

The answer of Use tests for symmetry to determine if...

Question 14

Find the equation of the circle that satisfies the conditions: A)(x + 2)² + (y - 8)² = 6 B)(x - 2)² + (y + 8)² = 36 C)(x - 2)² + (y + 8)² = 6 D)(x + 2)² + (y + 8)² = 36 E)(x + 2)² - (y + 8)² = 36

Accepted Answer

The answer of Find the equation of the circle that...

Question 15

Find the graph of the line through  for the value of  = 
A) 
B) 
C) 
D) 
E)

Accepted Answer

The answer of Find the graph of the line through...

Question 16

Sketch the graphs of the lines on the same coordinate plane. 
A) 
B) 
C) 
D) 
E)

Accepted Answer

The answer of Sketch the graphs of the lines on...

Question 17

Find the distance d (A, B) between the points A (3, - 2) and B (8, 3).
A)6.77
B)6.07
C)7.07
D)7.57
E)6.97

Accepted Answer

The distance between two points $(x_1, y_1)$ and $(x_2, y_2)$ in a plane is given by the formula $\sqrt{(x_2 - x_1)^2 + (y_2 - y_1)^2}$. For points A(3, -2) and B(8, 3), the distance is $\sqrt{(8 - 3)^2 + (3 - (-2))^2} = \sqrt{5^2 + 5^2} = \sqrt{50} = 7.07$.

Question 18

A college student receives an interest-free loan of $8,875 from a relative. The student will repay $155 per month until the loan is paid off. After how many months will the student owe $5,000?
A)after 32 months.
B)after 26 months.
C)after 22 months.
D)after 25 months.
E)after 12.5 months.

Accepted Answer

To find out after how many months the student will owe $5,000, we can calculate the total amount paid until the loan reduces to this amount. Starting with an $8,875 loan, subtracting $5,000 gives us $3,875, which is the amount the student will have paid off. Dividing this amount by the monthly payment of $155 gives us $3,875 / $155 = 25. Therefore, it will take 25 months for the student to owe $5,000.

Question 19

Sketch the graph of f 
A) 
B) 
C) 
D)

Accepted Answer

The answer of Sketch the graph of f 
A) 
B)...

Question 20

Given A (7, -3) and B (-9, 9), find the point on segment AB that is three-fourths of the way from A to B.
A)( 3, 0 )
B)( -6, 3 )
C)( -5, 6 )
D)( 6, -5 )
E)( 0, 3 )

Accepted Answer

To find the point that is three-fourths of the way from A to B, we use the formula for finding a point P(x, y) that divides the segment AB in the ratio m:n, which is $P(x, y) = \left(\frac{mx_2 + nx_1}{m + n}, \frac{my_2 + ny_1}{m + n}\right)$. Here, $x_1, y_1$ are the coordinates of A, and $x_2, y_2$ are the coordinates of B. Since the point is three-fourths of the way from A to B, the ratio m:n is 3:1. Plugging in the values, we get $P(x, y) = \left(\frac{3(-9) + 1(7)}{3 + 1}, \frac{3(9) + 1(-3)}{3 + 1}\right) = \left(\frac{-27 + 7}{4}, \frac{27 - 3}{4}\right) = \left(\frac{-20}{4}, \frac{24}{4}\right) = (-5, 6)$.

Quiz 3: Functions and Graphs

Find the domain of

Find the midpoint of the segment AB between the points A (- 3, - 5) and B (15, 7)

Let y = f (x) be a function with domain D = [ -6, -3 ] and range R = [ -8, -2 ]. Find the domain D and range R for the function

Find the domain of

Express the function in the form of .

Express the function in the form of

If are real numbers, find

Given the two lines graphed on the same coordinate plane, find the coordinates of the point of intersection (the coordinates are integers) .

Consider the following equations and their graph. Express, in interval form, the x-values such that Y₁ > Y₂ . Assume that the x- and y-values of each point of intersection are integers.

Find the point with coordinates of the form (2a, a) that is in the third quadrant and is a distance 9 from P(3, 4) .

Use tests for symmetry to determine if the graph of the function is symmetric with respect to the y-axis, the x-axis, or the origin.

Find the equation of the circle that satisfies the conditions:

Find the graph of the line through for the value of =

Sketch the graphs of the lines on the same coordinate plane.

Find the distance d (A, B) between the points A (3, - 2) and B (8, 3) .

A college student receives an interest-free loan of $8,875 from a relative. The student will repay $155 per month until the loan is paid off. After how many months will the student owe $5,000?

Sketch the graph of f

Given A (7, -3) and B (-9, 9) , find the point on segment AB that is three-fourths of the way from A to B.

Quiz 3: Functions and Graphs

Find the domain of

Find the midpoint of the segment AB between the points A (- 3, - 5) and B (15, 7)

Let y = f (x) be a function with domain D = [ -6, -3 ] and range R = [ -8, -2 ]. Find the domain D and range R for the function

Find the domain of

Express the function in the form of .

Express the function in the form of

If are real numbers, find

Given the two lines graphed on the same coordinate plane, find the coordinates of the point of intersection (the coordinates are integers) .

Consider the following equations and their graph. Express, in interval form, the x-values such that Y 1 > Y 2 . Assume that the x- and y-values of each point of intersection are integers.

Find the point with coordinates of the form (2a, a) that is in the third quadrant and is a distance 9 from P(3, 4) .

Use tests for symmetry to determine if the graph of the function is symmetric with respect to the y-axis, the x-axis, or the origin.

Find the equation of the circle that satisfies the conditions:

Find the graph of the line through for the value of =

Sketch the graphs of the lines on the same coordinate plane.

Find the distance d (A, B) between the points A (3, - 2) and B (8, 3) .

A college student receives an interest-free loan of $8,875 from a relative. The student will repay $155 per month until the loan is paid off. After how many months will the student owe $5,000?

Sketch the graph of f

Given A (7, -3) and B (-9, 9) , find the point on segment AB that is three-fourths of the way from A to B.

Consider the following equations and their graph. Express, in interval form, the x-values such that Y₁ > Y₂ . Assume that the x- and y-values of each point of intersection are integers.