Questions: Analyzing Function Behavior For each table below, select whether the data represents a function. If it does represent a function, determine if the function is increasing, decreasing or constant. x y 3 182 4 168 5 150 6 128 7 102 8 72 Select an answer x y 3 18 4 32 5 50 6 72 7 98 8 128 Select an answer x y 3 17 4 19 5 21 6 23 4 25 8 27 Select an answer x y 3 -7 4 -7 5 -7 6 -7 7 -7 8 -7 Select an answer

Analyzing Function Behavior
For each table below, select whether the data represents a function. If it does represent a function, determine if the function is increasing, decreasing or constant.

x y
3 182
4 168
5 150
6 128
7 102
8 72

Select an answer

x y
3 18
4 32
5 50
6 72
7 98
8 128

Select an answer

x y
3 17
4 19
5 21
6 23
4 25
8 27

Select an answer

x y
3 -7
4 -7
5 -7
6 -7
7 -7
8 -7

Select an answer

Transcript text: Analyzing Function Behavior For each table below, select whether the data represents a function. If it does represent a function, determine if the function is increasing, decreasing or constant. \begin{tabular}{|c|c|} \hline$x$ & $y$ \\ \hline 3 & 182 \\ \hline 4 & 168 \\ \hline 5 & 150 \\ \hline 6 & 128 \\ \hline 7 & 102 \\ \hline 8 & 72 \\ \hline \end{tabular} Select an answer \begin{tabular}{|c|c|} \hline$x$ & $y$ \\ \hline 3 & 18 \\ \hline 4 & 32 \\ \hline 5 & 50 \\ \hline 6 & 72 \\ \hline 7 & 98 \\ \hline 8 & 128 \\ \hline \end{tabular} \begin{tabular}{|c|c|} \hline$x$ & $y$ \\ \hline 3 & 17 \\ \hline 4 & 19 \\ \hline 5 & 21 \\ \hline 6 & 23 \\ \hline 4 & 25 \\ \hline 8 & 27 \\ \hline \end{tabular} Select an answer \begin{tabular}{|c|c|} \hline$x$ & $y$ \\ \hline 3 & -7 \\ \hline 4 & -7 \\ \hline 5 & -7 \\ \hline 6 & -7 \\ \hline 7 & -7 \\ \hline 8 & -7 \\ \hline \end{tabular} Select an answer

Solution

Solution Steps

To determine if the data represents a function, we need to check if each input $ x $ has a unique output $ y $. If it does, we then check if the function is increasing, decreasing, or constant by examining the trend of the $ y $ values as $ x $ increases.

Solution Approach

For each table, check if each $ x $ value maps to a unique $ y $ value.
If it is a function, determine if the $ y $ values are increasing, decreasing, or constant as $ x $ increases.

Step 1: Check if Each Table Represents a Function

To determine if each table represents a function, we need to check if each input $ x $ has a unique output $ y $.

For the first table: \[ \begin{array}{|c|c|} \hline x & y \\ \hline 3 & 182 \\ 4 & 168 \\ 5 & 150 \\ 6 & 128 \\ 7 & 102 \\ 8 & 72 \\ \hline \end{array} \] Each $ x $ value is unique, so it represents a function.
For the second table: \[ \begin{array}{|c|c|} \hline x & y \\ \hline 3 & 18 \\ 4 & 32 \\ 5 & 50 \\ 6 & 72 \\ 7 & 98 \\ 8 & 128 \\ \hline \end{array} \] Each $ x $ value is unique, so it represents a function.
For the third table: \[ \begin{array}{|c|c|} \hline x & y \\ \hline 3 & 17 \\ 4 & 19 \\ 5 & 21 \\ 6 & 23 \\ 4 & 25 \\ 8 & 27 \\ \hline \end{array} \] The $ x $ value 4 is repeated with different $ y $ values (19 and 25), so it does not represent a function.
For the fourth table: \[ \begin{array}{|c|c|} \hline x & y \\ \hline 3 & -7 \\ 4 & -7 \\ 5 & -7 \\ 6 & -7 \\ 7 & -7 \\ 8 & -7 \\ \hline \end{array} \] Each $ x $ value is unique, so it represents a function.

Step 2: Determine if the Function is Increasing, Decreasing, or Constant

For the tables that represent functions, we need to determine if the $ y $ values are increasing, decreasing, or constant as $ x $ increases.

For the first table: \[ \begin{array}{|c|c|} \hline x & y \\ \hline 3 & 182 \\ 4 & 168 \\ 5 & 150 \\ 6 & 128 \\ 7 & 102 \\ 8 & 72 \\ \hline \end{array} \] The $ y $ values are decreasing as $ x $ increases, so the function is decreasing.
For the second table: \[ \begin{array}{|c|c|} \hline x & y \\ \hline 3 & 18 \\ 4 & 32 \\ 5 & 50 \\ 6 & 72 \\ 7 & 98 \\ 8 & 128 \\ \hline \end{array} \] The $ y $ values are increasing as $ x $ increases, so the function is increasing.
For the fourth table: \[ \begin{array}{|c|c|} \hline x & y \\ \hline 3 & -7 \\ 4 & -7 \\ 5 & -7 \\ 6 & -7 \\ 7 & -7 \\ 8 & -7 \\ \hline \end{array} \] The $ y $ values are constant as $ x $ increases, so the function is constant.