Math / Algebra

QuestionVALUATE
Independent Practice \begin{tabular}{l|l|} \hline earning Goal & Lesson Reflection (circle one) \\ \hline \begin{tabular}{l} I can determine if a relation is a function. I can \\ represent a function using a graph and table. \end{tabular} & Starting... Getting There... Got it! \\ \hline \end{tabular} Complete the previous problems, check your solutions, then complete the Lesson Checkpoint below. Complete the Lesson Reflection above by circling your current understanding of the Learning Goal(s).
1. Determine whether each table represents a function. Select Function or Not a Function for each.
Table Function Not a Function \begin{tabular}{|c|c|c|c|c|} \hline $x$ & 2 & 3 & 4 & 5 \\ \hline $y$ & -3 & -3 & -3 & -4 \\ \hline \end{tabular} \begin{tabular}{|c|c|c|c|c|} \hline $x$ & -1 & -1 & -1 & -1 \\ \hline $y$ & 2 & 3 & 4 & 5 \\ \hline \end{tabular} \begin{tabular}{|c|c|c|c|c|} \hline $x$ & -6 & -4 & -3 & -2 \\ \hline $y$ & -11 & -11 & 10 & 15 \\ \hline \end{tabular} \begin{tabular}{|c|c|c|c|c|} \hline $x$ & -6 & 0 & 1 & -6 \\ \hline $y$ & 5 & 2 & 12 & 9 \\ \hline \end{tabular}
2. Which of the following could be a function? Select two that apply

Studdy Solution

STEP 1

What is this asking? We need to figure out which tables represent functions and pick out two more possible functions from a list. Watch out! Remember, a function means each input ( $x$ ) has only one output ( $y$ ).
If an $x$ value appears more than once with different $y$ values, it's not a function!

STEP 2

1. Analyze the tables
2. Identify potential functions

STEP 3

Let's look at the first table.
For every $x$ value, there's only one $y$ value. $x = 2$ goes to $y = -3$ , $x = 3$ goes to $y = -3$ , and so on.
Even though the $y$ values repeat, that's okay!
It's still a function!

STEP 4

Second table time!
Uh oh, $x = -1$ shows up multiple times with different $y$ values. $x = -1$ goes to $y = 2$ , $y = 3$ , $y = 4$ , and $y = 5$ .
Since one $x$ value has multiple $y$ values, this is not a function.

STEP 5

Third table!
Each $x$ has only one $y$ . $x = -6$ goes to $y = -11$ , $x = -4$ goes to $y = -11$ , $x = -3$ goes to $y = 10$ , and $x = -2$ goes to $y = 15$ .
This is a function!

STEP 6

Last table!
We see $x = -6$ twice, but with different $y$ values! $x = -6$ goes to both $y = 5$ and $y = 9$ .
This means it's not a function.

STEP 7

Since the problem text is missing the list of potential functions, I'll make up two examples that could be functions.

STEP 8

Example 1: $\{(1, 2), (2, 4), (3, 6)\}$ .
This is a function because each $x$ value (1, 2, and 3) has only one corresponding $y$ value.

STEP 9

Example 2: $\{(1, 2), (2, 2), (3, 2)\}$ .
This is also a function!
Even though all the $y$ values are the same, each $x$ still only has one $y$ value.

STEP 10

Table 1: Function Table 2: Not a Function Table 3: Function Table 4: Not a Function
Two examples of relations that could be functions: $\{(1, 2), (2, 4), (3, 6)\}$ and $\{(1, 2), (2, 2), (3, 2)\}$ .

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Studdy Solution

STEP 1

STEP 2

1. Analyze the tables
2. Identify potential functions

STEP 3

Let's look at the first table.
For every $x$ value, there's only one $y$ value. $x = 2$ goes to $y = -3$ , $x = 3$ goes to $y = -3$ , and so on.
Even though the $y$ values repeat, that's okay!
It's still a function!

STEP 4

Second table time!
Uh oh, $x = -1$ shows up multiple times with different $y$ values. $x = -1$ goes to $y = 2$ , $y = 3$ , $y = 4$ , and $y = 5$ .
Since one $x$ value has multiple $y$ values, this is not a function.

STEP 5

Third table!
Each $x$ has only one $y$ . $x = -6$ goes to $y = -11$ , $x = -4$ goes to $y = -11$ , $x = -3$ goes to $y = 10$ , and $x = -2$ goes to $y = 15$ .
This is a function!

STEP 6

Last table!
We see $x = -6$ twice, but with different $y$ values! $x = -6$ goes to both $y = 5$ and $y = 9$ .
This means it's not a function.

STEP 7

Since the problem text is missing the list of potential functions, I'll make up two examples that could be functions.

STEP 8

Example 1: $\{(1, 2), (2, 4), (3, 6)\}$ .
This is a function because each $x$ value (1, 2, and 3) has only one corresponding $y$ value.

STEP 9

Example 2: $\{(1, 2), (2, 2), (3, 2)\}$ .
This is also a function!
Even though all the $y$ values are the same, each $x$ still only has one $y$ value.

STEP 10

Table 1: Function Table 2: Not a Function Table 3: Function Table 4: Not a Function
Two examples of relations that could be functions: $\{(1, 2), (2, 4), (3, 6)\}$ and $\{(1, 2), (2, 2), (3, 2)\}$ .

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Studdy Solution

STEP 1

STEP 2

1. Analyze the tables2. Identify potential functions

STEP 3

Let's look at the first table.For every xxx value, there's only one yyy value. x=2x = 2x=2 goes to y=−3y = -3y=−3, x=3x = 3x=3 goes to y=−3y = -3y=−3, and so on.Even though the yyy values repeat, that's okay!It's still a **function**!

STEP 4

Second table time!Uh oh, x=−1x = -1x=−1 shows up multiple times with different yyy values. x=−1x = -1x=−1 goes to y=2y = 2y=2, y=3y = 3y=3, y=4y = 4y=4, and y=5y = 5y=5.Since one xxx value has multiple yyy values, this is *not* a **function**.

STEP 5

Third table!Each xxx has only one yyy. x=−6x = -6x=−6 goes to y=−11y = -11y=−11, x=−4x = -4x=−4 goes to y=−11y = -11y=−11, x=−3x = -3x=−3 goes to y=10y = 10y=10, and x=−2x = -2x=−2 goes to y=15y = 15y=15.This is a **function**!

STEP 6

Last table!We see x=−6x = -6x=−6 twice, but with different yyy values! x=−6x = -6x=−6 goes to both y=5y = 5y=5 and y=9y = 9y=9.This means it's *not* a **function**.

STEP 7

Since the problem text is missing the list of potential functions, I'll make up two examples that could be functions.

STEP 8

Example 1: {(1,2),(2,4),(3,6)}\{(1, 2), (2, 4), (3, 6)\}{(1,2),(2,4),(3,6)}.This *is* a **function** because each xxx value (1, 2, and 3) has only one corresponding yyy value.

STEP 9

Example 2: {(1,2),(2,2),(3,2)}\{(1, 2), (2, 2), (3, 2)\}{(1,2),(2,2),(3,2)}.This *is* also a **function**!Even though all the yyy values are the same, each xxx still only has one yyy value.

STEP 10

Table 1: **Function** Table 2: **Not a Function** Table 3: **Function** Table 4: **Not a Function**Two examples of relations that could be functions: {(1,2),(2,4),(3,6)}\{(1, 2), (2, 4), (3, 6)\}{(1,2),(2,4),(3,6)} and {(1,2),(2,2),(3,2)}\{(1, 2), (2, 2), (3, 2)\}{(1,2),(2,2),(3,2)}.

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1. Analyze the tables
2. Identify potential functions

Let's look at the first table.
For every $x$ value, there's only one $y$ value. $x = 2$ goes to $y = -3$ , $x = 3$ goes to $y = -3$ , and so on.
Even though the $y$ values repeat, that's okay!
It's still a function!

Second table time!
Uh oh, $x = -1$ shows up multiple times with different $y$ values. $x = -1$ goes to $y = 2$ , $y = 3$ , $y = 4$ , and $y = 5$ .
Since one $x$ value has multiple $y$ values, this is not a function.

Third table!
Each $x$ has only one $y$ . $x = -6$ goes to $y = -11$ , $x = -4$ goes to $y = -11$ , $x = -3$ goes to $y = 10$ , and $x = -2$ goes to $y = 15$ .
This is a function!

Last table!
We see $x = -6$ twice, but with different $y$ values! $x = -6$ goes to both $y = 5$ and $y = 9$ .
This means it's not a function.

Example 1: $\{(1, 2), (2, 4), (3, 6)\}$ .
This is a function because each $x$ value (1, 2, and 3) has only one corresponding $y$ value.

Example 2: $\{(1, 2), (2, 2), (3, 2)\}$ .
This is also a function!
Even though all the $y$ values are the same, each $x$ still only has one $y$ value.

Table 1: Function Table 2: Not a Function Table 3: Function Table 4: Not a Function
Two examples of relations that could be functions: $\{(1, 2), (2, 4), (3, 6)\}$ and $\{(1, 2), (2, 2), (3, 2)\}$ .