5. a function is defined as {(0,1),(2,3),(5,8),(7,2)}. which ordered pair can be added to the set to keep it a function?
a. (0,2) b. (7,0) c. (5,3) d. (1,3)
6. which set of ordered pairs represents a function?
a. {(0,4),(2,4),(2,5)}
b. {(6,0),(5,0),(4,0)}
c. {(4,1),(6,2),(6,3),(5,0)}
d. {(0,4),(1,4),(0,5),(1,5)}
7. which relation is not a function?
a. {(1,5),(2,6),(3,6),(4,7)}
b. {(4,7),(2,1),(-3,6),(3,4)}
c. {(-1,6),(1,3),(2,5),(1,7)}
d. {(-1,2),(0,5),(5,0),(2,-1)}
8. which statement is true about the relation shown on the graph?
a. it is a function because there exists one x - coordinate for each y - coordinate.
b. it is a function because there exists one y - coordinate for each x - coordinate.
c. it is not a function because there are multiple y - values for a given x - value.
d. it is not a function because there are multiple x - values for a given y - value.
9. which graph represents a function?
a.
b.
c.
d.
10. the two relations shown below are not functions. explain how you could change each relation so that it would become a function.
relation i:
relation ii:
{(-5,-2),(-4,0),(-2,1),(-1,3),(-4,4)}

Question

5. a function is defined as {(0,1),(2,3),(5,8),(7,2)}. which ordered pair can be added to the set to keep it a function?
a. (0,2)  b. (7,0)  c. (5,3)  d. (1,3)
6. which set of ordered pairs represents a function?
a. {(0,4),(2,4),(2,5)}
b. {(6,0),(5,0),(4,0)}
c. {(4,1),(6,2),(6,3),(5,0)}
d. {(0,4),(1,4),(0,5),(1,5)}
7. which relation is not a function?
a. {(1,5),(2,6),(3,6),(4,7)}
b. {(4,7),(2,1),(-3,6),(3,4)}
c. {(-1,6),(1,3),(2,5),(1,7)}
d. {(-1,2),(0,5),(5,0),(2,-1)}
8. which statement is true about the relation shown on the graph?
a. it is a function because there exists one x - coordinate for each y - coordinate.
b. it is a function because there exists one y - coordinate for each x - coordinate.
c. it is not a function because there are multiple y - values for a given x - value.
d. it is not a function because there are multiple x - values for a given y - value.
9. which graph represents a function?
a.
b.
c.
d.
10. the two relations shown below are not functions. explain how you could change each relation so that it would become a function.
relation i:
relation ii:
{(-5,-2),(-4,0),(-2,1),(-1,3),(-4,4)}

Accepted Answer

### Question 5
# Explanation:
## Step1: Recall function definition
A function is a relation where each input (x - value) has exactly one output (y - value). So we need to check which ordered pair has an x - value not already in the set $\{(0,1),(2,3),(5,8),(7,2)\}$ or, if the x - value is already present, the y - value is the same (but in this case, all existing x - values have unique y - values, so we need a new x - value or same x with same y, but same x with same y is trivial here). The x - values in the set are 0, 2, 5, 7.
## Step2: Check each option
- Option a: $(0,2)$ has x = 0, which is already in the set with y = 1. So can't add this as it would give x = 0 two different y - values.
- Option b: $(7,0)$ has x = 7, which is already in the set with y = 2. Can't add this.
- Option c: $(5,3)$ has x = 5, which is already in the set with y = 8. Can't add this.
- Option d: $(1,3)$ has x = 1, which is not in the set. So adding this will keep it a function as x = 1 has only one y - value (3).
# Answer: d. (1, 3)

### Question 6
# Explanation:
## Step1: Recall function definition
A function has each x - value with exactly one y - value.
## Step2: Check each option
- Option a: $\{(0,4),(2,4),(2,5)\}$ has x = 2 with y = 4 and y = 5. Not a function.
- Option b: $\{(6,0),(5,0),(4,0)\}$ has x = 6, 5, 4 each with one y - value (0). This is a function.
- Option c: $\{(4,1),(6,2),(6,3),(5,0)\}$ has x = 6 with y = 2 and y = 3. Not a function.
- Option d: $\{(0,4),(1,4),(0,5),(1,5)\}$ has x = 0 with y = 4 and y = 5, x = 1 with y = 4 and y = 5. Not a function.
# Answer: b. $\{(6,0),(5,0),(4,0)\}$

### Question 7
# Explanation:
## Step1: Recall function definition
A function has unique x - values (each x maps to one y).
## Step2: Check each option
- Option a: $\{(1,5),(2,6),(3,6),(4,7)\}$ Each x (1,2,3,4) has one y. Function.
- Option b: $\{(4,7),(2,1),(-3,6),(3,4)\}$ Each x (4,2, - 3,3) has one y. Function.
- Option c: $\{(-1,6),(1,3),(2,5),(1,7)\}$ x = 1 has y = 3 and y = 7. Not a function.
- Option d: $\{(-1,2),(0,5),(5,0),(2,-1)\}$ Each x (-1,0,5,2) has one y. Function.
# Answer: c. $\{(-1,6),(1,3),(2,5),(1,7)\}$

### Question 8
# Explanation:
## Step1: Recall vertical line test
A graph is a function if any vertical line intersects the graph at most once. The given graph is a circle. For a given x - value (inside the circle's horizontal range), there are two y - values (one above and one below the center).
## Step2: Analyze options
- Option a: Wrong, function is about x to y mapping, not y to x.
- Option b: Wrong, the graph fails vertical line test.
- Option c: Correct, because for a given x - value, there are multiple y - values (fails vertical line test).
- Option d: Wrong, the issue is multiple y for x, not multiple x for y.
# Answer: c. It is not a function because there are multiple y - values for a given x - value.

### Question 9
# Explanation:
## Step1: Recall vertical line test
A graph represents a function if no vertical line intersects it more than once.
## Step2: Check each graph
- Option a: The graph has a vertical line - like shape (two arrows for same x), so vertical line would intersect twice. Not a function.
- Option b: Two vertical lines, so vertical line (along that x) intersects twice. Not a function.
- Option c: A circle, vertical line intersects twice. Not a function.
- Option d: The graph is a V - shape, and any vertical line will intersect at most once. So this is a function.
# Answer: d

### Question 10
#### Relation I (Graph)
# Explanation:
## Step1: Identify the non - function part
In the graph of Relation I, we can see that there are horizontal segments (e.g., at y = 20, x ranges from 2 to 3, and at x = 3, there is a point at y = 30). Also, at x = 1, there is an open circle at y = 10 and no closed point? Wait, more precisely, the horizontal line (constant y for multiple x) and the fact that for some x, there are multiple y - values. To make it a function, we need to ensure each x has one y. So we can either:
- Adjust the horizontal segment: For example, change the horizontal line (y = 20 from x = 2 to x = 3) to a non - horizontal line, or assign a unique y - value to each x. Also, at x = 1, we can close the circle at y = 10 or remove the open circle and assign a y - value. Alternatively, for the part where x is in [2,3] and y = 20, we can make it a function by having each x in [2,3] map to a unique y (e.g., make it an increasing or decreasing function in that interval) and ensure that at x = 3, the point at y = 30 is consistent (i.e., for x = 3, only one y - value).
#### Relation II ($\{(-5,-2),(-4,0),(-2,1),(-1,3),(-4,4)\}$)
## Step2: Identify the non - function part
In Relation II, the x - value - 4 appears twice: $(-4,0)$ and $(-4,4)$. To make it a function, we need to ensure each x has one y. So we can either change the y - value of one of the $(-4,y)$ ordered pairs (e.g., change $(-4,4)$ to $(-3,4)$ so that x = - 4 has only y = 0, or change $(-4,0)$ to another x - value like $(-3,0)$) or remove one of the ordered pairs with x = - 4.
# Brief Explanations (for both relations):
- **Relation I**: The graph has horizontal segments (multiple y for same x) and inconsistent points. To fix, ensure each x has one y: adjust horizontal parts to be non - horizontal (unique y per x), resolve the open/closed point at x = 1, and ensure x = 3 has one y. For example, make the horizontal line (y = 20) a function (e.g., linear from (2,20) to (3,20) is still horizontal, so better to make it a curve or assign a single y to x in that range; also, at x = 1, add a closed point at y = 10 or define y at x = 1, and ensure x = 3 has only y = 30 (remove the horizontal part's conflict with x = 3's y = 30)).
- **Relation II**: The ordered pair $(-4,0)$ and $(-4,4)$ have the same x ($-4$) with different y. To fix, either change the x - value of one of these pairs (e.g., make one $(-3,0)$ or $(-3,4)$) or remove one of the pairs, so that x = - 4 has only one y - value.
# Answer:
- **Relation I**: Adjust the graph to ensure each $x$ - value has exactly one $y$ - value. For example, modify the horizontal segment (e.g., replace the horizontal line at $y = 20$ with a non - horizontal curve, resolve the open/closed point at $x = 1$, and ensure $x = 3$ has only one $y$ - value).
- **Relation II**: Change one of the ordered pairs with $x=-4$ (e.g., replace $(-4,0)$ with $(-3,0)$ or $(-4,4)$ with $(-3,4)$) or remove one of the pairs $(-4,0)$ or $(-4,4)$ so that $x = - 4$ has only one $y$ - value.

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Explanation:

Question 5

Step1: Recall function definition

Step2: Check each option

Step1: Recall function definition

Step2: Check each option

Step1: Recall function definition

Step2: Check each option

Answer:

Question 6