Question 1

Find the equation of a circle with center (2, -3) and the graph of which contains the point (3, 4), then sketch its graph.

Accepted Answer

(x - 2)² + (y + 3)² = 50 (Gridlines are spaced one unit apart.)

Question 2

Write the equation in factored form to find the center and radius of the circle. Then sketch the graph. x² + y² + 6x - 8 = 0 A) (x + 3)² + y² = 16 (Gridlines are spaced one unit apart.) B) (x + 3)² + y² = 17 (Gridlines are spaced one unit apart.) C) (x - 3)² + y² = 16 (Gridlines are spaced one unit apart.) D) (x - 3)² + y² = 17 (Gridlines are spaced one unit apart.)

Accepted Answer

B

Question 3

Use the distance formula to find the length of the line segment.  (Gridlines are spaced one unit apart.)
A) 7
B) 
C) 
D)

Accepted Answer

C

Question 4

Find the equation of a circle whose diameter has endpoints (2, -7) and (2, 1), then sketch its graph.

Accepted Answer

The answer of Find the equation of a circle whose...

Question 5

Determine whether the mapping represents a function or nonfunction. If a nonfunction, explain how the definition of a function is violated. 
A) Function.
B) Not a function. Amy is paired with two parents.
C) Not a function. Two children are paired with Bob.
D) Not a function. Some parents are paired with only one child.

Accepted Answer

A function is a mapping that assigns exactly one output to each input. In this case, Amy is paired with two parents, violating the rule of assigning only one output to each input, which makes it a nonfunction.

Question 6

Determine whether the relation represents a function or a nonfunction. If the relation is a nonfunction, explain how the definition of a function is violated. {(2, -5), (-1, -4), (4, -7), (1, -2), (-1, -6), (6, -8)}
A) Function
B) Not a function; -1 is paired with -4 and -6.

Accepted Answer

The relation is not a function because the input value of -1 is paired with two different output values (-4 and -6), which violates the definition of a function.

Question 7

Find the equation of a circle with center (-7, 6) and radius . A) (x + 7)² + (y - 6)² = B) (x - 7)² + (y + 6)² = C) (x + 7)² + (y - 6)² = 5 D) (x - 7)² + (y + 6)² = 5

Accepted Answer

The answer of Find the equation of a circle with...

Question 8

Find the midpoint of the segment with endpoints (5, 7) and (3, -5).
A) (8, 2)
B) (2, 12)
C) (4, 1)
D) (1, 6)

Accepted Answer

To find the midpoint of a segment, we take the average of the x-coordinates and the average of the y-coordinates.

Average of x-coordinates = (5+3)/2 = 4
Average of y-coordinates = (7+(-5))/2 = 1

Therefore, the midpoint is (4, 1), which is Choice C.

Question 9

Complete the table using the given equation. Use these points to graph the relation.

Accepted Answer

The answer of Complete the table using the given equation....

Question 10

Find the equation of a circle with center (0, 0) and radius 10.

Accepted Answer

The answer of Find the equation of a circle with...

Question 11

Identify the center and radius of the circle, then graph. Also, state the domain and range of the relation. (x - 2)² + (y - 1)² = 9

Accepted Answer

The answer of Identify the center and radius of the...

Question 12

Identify the center and radius of the circle. x² + (y - 8)² = 4.

Accepted Answer

The answer of Identify the center and radius of the...

Question 13

Identify the center and radius of the circle. (x + 6)² + (y - 4)² = 16. A) center (-6, 4) and radius 4 B) center (6, -4) and radius 4 C) center (-6, 4) and radius 16 D) center (6, -4) and radius 16

Accepted Answer

We can rewrite the equation as:

(x + 6)² + (y - 4)² = 16

This is the equation of a circle with center (-6, 4) and radius 4. Therefore, the correct answer is A.

Question 14

Find the equation of a circle with center (-1, 2) and radius  . Then sketch its graph.

Accepted Answer

The answer of Find the equation of a circle with...

Question 15

Complete the table using the given equation. If an x input corresponds to two possible y outputs, be sure to find both.
|y - 3| = x

Accepted Answer

The answer of Complete the table using the given equation....

Question 16

Find the equation of a circle with center (0, 0) and radius 4. Then sketch its graph.

Accepted Answer

The answer of Find the equation of a circle with...

Question 17

Find the equation of a circle with center (0, 2) and radius . Then sketch its graph. A) x² + (y - 2)² = (Gridlines are spaced one unit apart.) B) x² + (y - 2)² = 6 (Gridlines are spaced one unit apart.) C) x² + (y - 2)² = (Gridlines are spaced one unit apart.) D) x² + (y - 2)² = 6 (Gridlines are spaced one unit apart.)

Accepted Answer

The answer of Find the equation of a circle with...

Question 18

Determine whether the relation represents a function or a nonfunction. If the relation is a nonfunction, explain how the definition of a function is violated. {(-9, 10), (-12, 11), (-7, 8), (-10, 13), (-13, 11), (-5, 7)}
A) Function
B) Nonfunction; -12 and -13 are both paired with 11.

Accepted Answer

Each input (-9, -12, -7, -10, -13, -5) is paired with exactly one output, so the relation is a function.

Question 19

Write the equation in factored form to find the center and radius of the circle. x² + y² + 14x - 2y + 3 = 0

Accepted Answer

The answer of Write the equation in factored form to...

Question 20

State the domain and range of the relation.
{(5, 8), (6, 9), (7, 10), (8, 11)}

Accepted Answer

The answer of State the domain and range of the...

Quiz 2: Relations, Functions and Graphs

Find the equation of a circle with center (2, -3) and the graph of which contains the point (3, 4), then sketch its graph.

Write the equation in factored form to find the center and radius of the circle. Then sketch the graph. x² + y² + 6x - 8 = 0

Use the distance formula to find the length of the line segment. (Gridlines are spaced one unit apart.)

Find the equation of a circle whose diameter has endpoints (2, -7) and (2, 1), then sketch its graph.

Determine whether the mapping represents a function or nonfunction. If a nonfunction, explain how the definition of a function is violated.

Determine whether the relation represents a function or a nonfunction. If the relation is a nonfunction, explain how the definition of a function is violated. {(2, -5) , (-1, -4) , (4, -7) , (1, -2) , (-1, -6) , (6, -8) }

Find the equation of a circle with center (-7, 6) and radius .

Find the midpoint of the segment with endpoints (5, 7) and (3, -5) .

Complete the table using the given equation. Use these points to graph the relation.

Find the equation of a circle with center (0, 0) and radius 10.

Identify the center and radius of the circle, then graph. Also, state the domain and range of the relation. (x - 2)² + (y - 1)² = 9

Identify the center and radius of the circle. x² + (y - 8)² = 4.

Identify the center and radius of the circle. (x + 6) ² + (y - 4) ² = 16.

Find the equation of a circle with center (-1, 2) and radius . Then sketch its graph.

Complete the table using the given equation. If an x input corresponds to two possible y outputs, be sure to find both. |y - 3| = x

Find the equation of a circle with center (0, 0) and radius 4. Then sketch its graph.

Find the equation of a circle with center (0, 2) and radius . Then sketch its graph.

Determine whether the relation represents a function or a nonfunction. If the relation is a nonfunction, explain how the definition of a function is violated. {(-9, 10) , (-12, 11) , (-7, 8) , (-10, 13) , (-13, 11) , (-5, 7) }

Write the equation in factored form to find the center and radius of the circle. x² + y² + 14x - 2y + 3 = 0

State the domain and range of the relation. {(5, 8), (6, 9), (7, 10), (8, 11)}

Quiz 2: Relations, Functions and Graphs

Find the equation of a circle with center (2, -3) and the graph of which contains the point (3, 4), then sketch its graph.

Write the equation in factored form to find the center and radius of the circle. Then sketch the graph. x2 + y2 + 6x - 8 = 0

Use the distance formula to find the length of the line segment. (Gridlines are spaced one unit apart.)

Find the equation of a circle whose diameter has endpoints (2, -7) and (2, 1), then sketch its graph.

Determine whether the mapping represents a function or nonfunction. If a nonfunction, explain how the definition of a function is violated.

Determine whether the relation represents a function or a nonfunction. If the relation is a nonfunction, explain how the definition of a function is violated. {(2, -5) , (-1, -4) , (4, -7) , (1, -2) , (-1, -6) , (6, -8) }

Find the equation of a circle with center (-7, 6) and radius .

Find the midpoint of the segment with endpoints (5, 7) and (3, -5) .

Complete the table using the given equation. Use these points to graph the relation.

Find the equation of a circle with center (0, 0) and radius 10.

Identify the center and radius of the circle, then graph. Also, state the domain and range of the relation. (x - 2)2 + (y - 1)2 = 9

Identify the center and radius of the circle. x2 + (y - 8)2 = 4.

Identify the center and radius of the circle. (x + 6) 2 + (y - 4) 2 = 16.

Find the equation of a circle with center (-1, 2) and radius . Then sketch its graph.

Complete the table using the given equation. If an x input corresponds to two possible y outputs, be sure to find both. |y - 3| = x

Find the equation of a circle with center (0, 0) and radius 4. Then sketch its graph.

Find the equation of a circle with center (0, 2) and radius . Then sketch its graph.

Determine whether the relation represents a function or a nonfunction. If the relation is a nonfunction, explain how the definition of a function is violated. {(-9, 10) , (-12, 11) , (-7, 8) , (-10, 13) , (-13, 11) , (-5, 7) }

Write the equation in factored form to find the center and radius of the circle. x2 + y2 + 14x - 2y + 3 = 0

State the domain and range of the relation. {(5, 8), (6, 9), (7, 10), (8, 11)}

Write the equation in factored form to find the center and radius of the circle. Then sketch the graph. x² + y² + 6x - 8 = 0

Identify the center and radius of the circle, then graph. Also, state the domain and range of the relation. (x - 2)² + (y - 1)² = 9

Identify the center and radius of the circle. x² + (y - 8)² = 4.

Identify the center and radius of the circle. (x + 6) ² + (y - 4) ² = 16.

Write the equation in factored form to find the center and radius of the circle. x² + y² + 14x - 2y + 3 = 0