Answered

Get the best answers to your questions with the help of IDNLearn.com's experts. Ask your questions and receive prompt, detailed answers from our experienced and knowledgeable community members.

Copy and complete the table by filling in the blank spaces using the given equations. Write down the domain of the input values.

a. [tex]\(y = 2 \times x + 1\)[/tex]

\begin{tabular}{|l|l|l|l|l|l|l|l|}
\hline
Input [tex]$(x)$[/tex] & 0 & 1 & 2 & 3 & 4 & 5 & 6 \\
\hline
Output [tex]$(y)$[/tex] & 1 & 3 & 5 & 7 & 9 & 11 & 13 \\
\hline
\end{tabular}

b. [tex]\(y = 5 \times x\)[/tex]

\begin{tabular}{|l|l|l|l|l|l|l|l|}
\hline
Input [tex]$(x)$[/tex] & -3 & -2 & -1 & 0 & 1 & 2 & 3 \\
\hline
Output [tex]$(y)$[/tex] & -15 & -10 & -5 & 0 & 5 & 10 & 15 \\
\hline
\end{tabular}

c. [tex]\(y = -2 \times x\)[/tex]

\begin{tabular}{|l|l|l|l|l|l|l|l|}
\hline
Input [tex]$(x)$[/tex] & -5 & -3 & -1 & 0 & 2 & 4 & 5 \\
\hline
Output [tex]$(y)$[/tex] & 10 & 6 & 2 & 0 & -4 & -8 & -10 \\
\hline
\end{tabular}

d. [tex]\(y = \frac{1}{2} \times x + 2\)[/tex]

\begin{tabular}{|l|l|l|l|l|l|}
\hline
Input [tex]$(x)$[/tex] & -12 & -6 & 0 & 4 & 8 \\
\hline
Output [tex]$(y)$[/tex] & -4 & -1 & 2 & 4 & 6 \\
\hline
\end{tabular}

e. [tex]\(y = 8 - x\)[/tex]

\begin{tabular}{|l|l|l|l|l|l|}
\hline
Input [tex]$(x)$[/tex] & 0 & 2 & 4 & 6 & 8 \\
\hline
Output [tex]$(y)$[/tex] & 8 & 6 & 4 & 2 & 0 \\
\hline
\end{tabular}

Domain of the input values: [tex]\([-12, -6, 0, 4, 8]\)[/tex]

Sagot :

GinnyAnsweridn
Let's go through each part of the question step by step.

### Part d
For the equation [tex]\( y = 2 \times x + 1 \)[/tex] when [tex]\( x = 5 \)[/tex]:

[tex]\[ y = 2 \times 5 + 1 = 10 + 1 = 11 \][/tex]

So, [tex]\( y = 11 \)[/tex] when [tex]\( x = 5 \)[/tex].

### Part e
For the equation [tex]\( y = 8 - x \)[/tex] when [tex]\( x = 2 \)[/tex]:

[tex]\[ y = 8 - 2 = 6 \][/tex]

So, [tex]\( y = 6 \)[/tex] when [tex]\( x = 2 \)[/tex].

### Completing Tables and Writing the Domain

#### Part a: [tex]\( y = 2 \times x + 1 \)[/tex]

Given the input values and part of the output:
[tex]\[ x = [0, 1, 2, 4, 5, 3] \][/tex]
[tex]\[ y = [1, 3, 5, 9, 11, 13] \][/tex]

Let's fill in the table:
\begin{tabular}{|l|l|l|l|l|l|l|l|}
\hline Input [tex]$(x)$[/tex] & 0 & 1 & 2 & 3 & 4 & 5 & \\
\hline Output [tex]$(y)$[/tex] & 1 & 3 & 5 & 13 & 9 & 11 & \\
\hline
\end{tabular}

Domain of [tex]\(x\)[/tex]: [tex]\(\{0, 1, 2, 3, 4, 5\}\)[/tex].

#### Part b: [tex]\( y = 5 \times x \)[/tex]

Given the input values and part of the output:
[tex]\[ x = [-3, -2, -1, 2, 0, 1, 3] \][/tex]
[tex]\[ y = [-15, -10, 0, 5, 15] \][/tex]

Let's fill in the table:
\begin{tabular}{|l|l|l|l|l|l|l|l|}
\hline Input [tex]$(x)$[/tex] & -3 & -2 & -1 & 0 & 1 & 2 & 3 \\
\hline Output [tex]$(y)$[/tex] & -15 & -10 & -5 & 0 & 5 & 10 & 15 \\
\hline
\end{tabular}

Domain of [tex]\(x\)[/tex]: [tex]\(\{-3, -2, -1, 0, 1, 2, 3\}\)[/tex].

#### Part c: [tex]\( y = -2 \times x \)[/tex]

Given the input values and part of the output:
[tex]\[ x = [-5, -3, -1, 0, 4] \][/tex]
[tex]\[ y = [6, 2, 0, -8] \][/tex]

Let's fill in the table:
\begin{tabular}{|l|l|l|l|l|l|l|l|}
\hline Input [tex]$(x)$[/tex] & -5 & -3 & -1 & 0 & 2 & 4 & \\
\hline Output [tex]$(y)$[/tex] & 10 & 6 & 2 & 0 & -4 & -8 & -10 \\
\hline
\end{tabular}

Domain of [tex]\(x\)[/tex]: [tex]\(\{-5, -3, -1, 0, 2, 4\}\)[/tex].

#### Part d: [tex]\( y = \frac{1}{2} \times x + 2 \)[/tex]

Given the input values and part of the output:
[tex]\[ x = [-13, -12, 0, 1, -11] \][/tex]
[tex]\[ y = [-4.0, 2.0, 2.5] \][/tex]

Let's fill in the table:
\begin{tabular}{|l|l|l|l|l|l|}
\hline Input [tex]$(x)$[/tex] & -13 & -12 & 0 & 1 & -11 \\
\hline Output [tex]$(y)$[/tex] & -4.5 & -4.0 & 2.0 & 2.5 & -3.5 \\
\hline
\end{tabular}

Domain of [tex]\(x\)[/tex]: [tex]\(\{-13, -12, -11, 0, 1\}\)[/tex].

This completes the solution, matching provided numerical calculations.
Your participation means a lot to us. Keep sharing information and solutions. This community grows thanks to the amazing contributions from members like you. Find precise solutions at IDNLearn.com. Thank you for trusting us with your queries, and we hope to see you again.