Type The Correct Answer In Each Box. Use Numerals Instead Of Words.The Domain Of This Function Is { − 12 , − 6 , 3 , 15 } \{-12, -6, 3, 15\} { − 12 , − 6 , 3 , 15 } . Y = − 2 3 Z + 7 Y = -\frac{2}{3} Z + 7 Y = − 3 2 ​ Z + 7 Complete The Table Based On The Given Domain. \[ \begin{tabular}{|c|c|} \hline X$ &

Domain and Function

The given function is $y = -\frac{2}{3} z + 7$. However, the domain of the function is given as $\{-12, -6, 3, 15\}$, but it seems that there is a mistake in the function. It should be $y = -\frac{2}{3} x + 7$ instead of $y = -\frac{2}{3} z + 7$. Assuming this is the correct function, we will proceed with completing the table.

Completing the Table

To complete the table, we need to substitute each value of $x$ from the domain into the function $y = -\frac{2}{3} x + 7$ and calculate the corresponding value of $y$.

Substituting $x = -12$

$y = -\frac{2}{3} (-12) + 7$ $y = \frac{24}{3} + 7$ $y = 8 + 7$ $y = 15$

Substituting $x = -6$

$y = -\frac{2}{3} (-6) + 7$ $y = \frac{12}{3} + 7$ $y = 4 + 7$ $y = 11$

Substituting $x = 3$

$y = -\frac{2}{3} (3) + 7$ $y = -2 + 7$ $y = 5$

Substituting $x = 15$

$y = -\frac{2}{3} (15) + 7$ $y = -10 + 7$ $y = -3$

Completed Table

$x$	$y$
-12	15
-6	11
3	5
15	-3

Discussion Category: Mathematics

The given problem involves completing a table based on a given function and domain. This requires understanding of algebraic functions and substitution. The function $y = -\frac{2}{3} x + 7$ is a linear function, and the domain is a set of discrete values. The table is completed by substituting each value of $x$ into the function and calculating the corresponding value of $y$. This type of problem is commonly encountered in mathematics, particularly in algebra and calculus.

Domain and Function

The given function is $y = -\frac{2}{3} x + 7$. However, the domain of the function is given as $\{-12, -6, 3, 15\}$, but it seems that there is a mistake in the function. It should be $y = -\frac{2}{3} x + 7$ instead of $y = -\frac{2}{3} z + 7$. Assuming this is the correct function, we will proceed with completing the table.

Completing the Table

To complete the table, we need to substitute each value of $x$ from the domain into the function $y = -\frac{2}{3} x + 7$ and calculate the corresponding value of $y$.

Substituting $x = -12$

$y = -\frac{2}{3} (-12) + 7$ $y = \frac{24}{3} + 7$ $y = 8 + 7$ $y = 15$

Substituting $x = -6$

$y = -\frac{2}{3} (-6) + 7$ $y = \frac{12}{3} + 7$ $y = 4 + 7$ $y = 11$

Substituting $x = 3$

$y = -\frac{2}{3} (3) + 7$ $y = -2 + 7$ $y = 5$

Substituting $x = 15$

$y = -\frac{2}{3} (15) + 7$ $y = -10 + 7$ $y = -3$

Completed Table

$x$	$y$
-12	15
-6	11
3	5
15	-3

Discussion Category: Mathematics

The given problem involves completing a table based on a given function and domain. This requires understanding of algebraic functions and substitution. The function $y = -\frac{2}{3} x + 7$ is a linear function, and the domain is a set of discrete values. The table is completed by substituting each value of $x$ into the function and calculating the corresponding value of $y$. This type of problem is commonly encountered in mathematics, particularly in algebra and calculus.

Q&A

Q1: What is the given function?

A1: The given function is $y = -\frac{2}{3} x + 7$.

Q2: What is the domain of the function?

A2: The domain of the function is $\{-12, -6, 3, 15\}$.

Q3: How do you complete the table?

A3: To complete the table, substitute each value of $x$ from the domain into the function $y = -\frac{2}{3} x + 7$ and calculate the corresponding value of $y$.

Q4: What is the value of $y$ when $x = -12$?

A4: The value of $y$ when $x = -12$ is 15.

Q5: What is the value of $y$ when $x = 15$?

A5: The value of $y$ when $x = 15$ is -3.

Q6: What type of function is $y = -\frac{2}{3} x + 7$?

A6: The function $y = -\frac{2}{3} x + 7$ is a linear function.

Q7: What is the significance of the domain in this problem?

A7: The domain is a set of discrete values that are used to substitute into the function to calculate the corresponding value of $y$.

Q8: What is the purpose of completing the table?

A8: The purpose of completing the table is to find the corresponding value of $y$ for each value of $x$ in the domain.

Q9: What is the relationship between the function and the table?

A9: The function and the table are related in that the function is used to calculate the corresponding value of $y$ for each value of $x$ in the domain, which is then used to complete the table.

Q10: What is the relevance of this problem to real-life situations?

A10: This problem is relevant to real-life situations where data is collected and analyzed, such as in science, engineering, and economics.