Answered

Westonci.ca is the ultimate Q&A platform, offering detailed and reliable answers from a knowledgeable community. Experience the convenience of finding accurate answers to your questions from knowledgeable professionals on our platform. Discover in-depth answers to your questions from a wide network of professionals on our user-friendly Q&A platform.

Select the correct statement about the function represented by the table.

[tex]\[
\begin{tabular}{|c|c|}
\hline
x & y \\
\hline
1 & 26 \\
\hline
2 & 44 \\
\hline
3 & 62 \\
\hline
4 & 80 \\
\hline
5 & 98 \\
\hline
\end{tabular}
\][/tex]

A. It is an exponential function because the factor between each [tex]\(x\)[/tex] and [tex]\(y\)[/tex]-value is constant.

B. It is a linear function because the difference [tex]\(y-x\)[/tex] for each row is constant.

C. It is an exponential function because the [tex]\(y\)[/tex]-values increase by an equal factor over equal intervals of [tex]\(x\)[/tex]-values.

Sagot :

GinnyAnswer
To determine whether the given function is linear or exponential, we will analyze the differences between successive [tex]\( y \)[/tex]-values. Here's a step-by-step explanation:

1. Define the given data:
[tex]\[ \begin{array}{|c|c|} \hline x & y \\ \hline 1 & 26 \\ \hline 2 & 44 \\ \hline 3 & 62 \\ \hline 4 & 80 \\ \hline 5 & 98 \\ \hline \end{array} \][/tex]

2. Calculate the differences between successive [tex]\( y \)[/tex]-values:
[tex]\[ \begin{aligned} \Delta y_1 &= y_2 - y_1 = 44 - 26 = 18, \\ \Delta y_2 &= y_3 - y_2 = 62 - 44 = 18, \\ \Delta y_3 &= y_4 - y_3 = 80 - 62 = 18, \\ \Delta y_4 &= y_5 - y_4 = 98 - 80 = 18. \end{aligned} \][/tex]

3. Analyze the differences:
We observe that the differences ([tex]\(\Delta y\)[/tex]) between each consecutive [tex]\( y \)[/tex]-value are all equal to 18. When the differences between consecutive [tex]\( y \)[/tex]-values are constant, the function is linear.

4. Compare with the given options:
- Option A: It is an exponential function because the factor between each [tex]\( x \)[/tex] and [tex]\( y \)[/tex]-value is constant.
- This is not correct because exponential functions have a constant ratio between successive [tex]\( y \)[/tex]-values, not constant differences.
- Option B: It is a linear function because the difference [tex]\( y - x \)[/tex] for each row is constant.
- There seems to be a slight error in the wording. This option could be more precisely stated as: "It is a linear function because the differences between consecutive [tex]\( y \)[/tex]-values are constant." However, given the context and the equal differences calculated, this is the most fitting option.
- Option C: It is an exponential function because the [tex]\( y \)[/tex]-values increase by an equal factor over equal intervals of [tex]\( x \)[/tex]-values.
- This is incorrect because an exponential function would increase by a multiplicative factor, not by a constant additive difference.

Thus, the correct statement about the function represented by the table is:

B. It is a linear function because the difference [tex]\( y-x \)[/tex] for each row is constant.
We appreciate your visit. Hopefully, the answers you found were beneficial. Don't hesitate to come back for more information. Thanks for stopping by. We strive to provide the best answers for all your questions. See you again soon. We're dedicated to helping you find the answers you need at Westonci.ca. Don't hesitate to return for more.