Welcome to Westonci.ca, the place where your questions find answers from a community of knowledgeable experts. Our platform connects you with professionals ready to provide precise answers to all your questions in various areas of expertise. Join our platform to connect with experts ready to provide precise answers to your questions in different areas.
Sagot :
To determine the type of function represented by the given table, we'll analyze the relationship between the [tex]\( x \)[/tex] and [tex]\( y \)[/tex] values. Here is the table for reference:
[tex]\[ \begin{array}{|c|c|c|c|c|c|c|} \hline x & 0 & 1 & 2 & 3 & 4 & 5 \\ \hline y & -7 & -2 & 3 & 8 & 13 & 18 \\ \hline \end{array} \][/tex]
### Step-by-Step Solution:
1. List the given [tex]\( x \)[/tex] and [tex]\( y \)[/tex] values:
[tex]\[ \begin{array}{|c|c|} \hline x & y \\ \hline 0 & -7 \\ 1 & -2 \\ 2 & 3 \\ 3 & 8 \\ 4 & 13 \\ 5 & 18 \\ \hline \end{array} \][/tex]
2. Calculate the differences between consecutive [tex]\( y \)[/tex]-values:
[tex]\[ \begin{array}{|c|c|c|} \hline x & y & \Delta y \\ \hline 0 & -7 & - \\ 1 & -2 & -2 - (-7) = 5 \\ 2 & 3 & 3 - (-2) = 5 \\ 3 & 8 & 8 - 3 = 5 \\ 4 & 13 & 13 - 8 = 5 \\ 5 & 18 & 18 - 13 = 5 \\ \hline \end{array} \][/tex]
So, the differences between consecutive [tex]\( y \)[/tex]-values are all 5.
3. Analyze the differences:
Since the differences between consecutive [tex]\( y \)[/tex]-values are constant (5), we have a consistent rate of change.
### Conclusion:
A function that has a constant rate of change in [tex]\( y \)[/tex] with respect to [tex]\( x \)[/tex] is a linear function.
Thus, the type of function represented by the table is linear.
[tex]\[ \begin{array}{|c|c|c|c|c|c|c|} \hline x & 0 & 1 & 2 & 3 & 4 & 5 \\ \hline y & -7 & -2 & 3 & 8 & 13 & 18 \\ \hline \end{array} \][/tex]
### Step-by-Step Solution:
1. List the given [tex]\( x \)[/tex] and [tex]\( y \)[/tex] values:
[tex]\[ \begin{array}{|c|c|} \hline x & y \\ \hline 0 & -7 \\ 1 & -2 \\ 2 & 3 \\ 3 & 8 \\ 4 & 13 \\ 5 & 18 \\ \hline \end{array} \][/tex]
2. Calculate the differences between consecutive [tex]\( y \)[/tex]-values:
[tex]\[ \begin{array}{|c|c|c|} \hline x & y & \Delta y \\ \hline 0 & -7 & - \\ 1 & -2 & -2 - (-7) = 5 \\ 2 & 3 & 3 - (-2) = 5 \\ 3 & 8 & 8 - 3 = 5 \\ 4 & 13 & 13 - 8 = 5 \\ 5 & 18 & 18 - 13 = 5 \\ \hline \end{array} \][/tex]
So, the differences between consecutive [tex]\( y \)[/tex]-values are all 5.
3. Analyze the differences:
Since the differences between consecutive [tex]\( y \)[/tex]-values are constant (5), we have a consistent rate of change.
### Conclusion:
A function that has a constant rate of change in [tex]\( y \)[/tex] with respect to [tex]\( x \)[/tex] is a linear function.
Thus, the type of function represented by the table is linear.
Thank you for your visit. We're committed to providing you with the best information available. Return anytime for more. Thanks for using our service. We're always here to provide accurate and up-to-date answers to all your queries. Thank you for visiting Westonci.ca, your go-to source for reliable answers. Come back soon for more expert insights.