Question 2 \begin{tabular}{|l|l|}\hline Which of the following statements are true? Check all that apply. \ $$ \square $$ The Average Rate of Change of a function over a specified interval is the ratio: \ $$ \frac{ ext { Change in Output }}{ ext { Change in Input }} $$. \ $$ \square $$ The Average Rate of Change is another term for Slope over a given interval. \ $$ \square $$ If the Average Rate of Change is the same between any two point of a function, then the function \ is Linear Function and the Average Rate of Change equals the Slope. \ $$ \square $$ Average Rate of Changeh $$ \frac{x_{2}-x_{1}}{y_{2}-y_{1}}=\frac{ ext { Change in } \mathrm{x}}{ ext { Change in } y}=\frac{\Delta x}{\Delta y} $$ \ $$ \square $$\end{tabular}

Question

Question 2 \begin{tabular}{|l|l|}\hline Which of the following statements are true? Check all that apply. \ $$ \square $$ The Average Rate of Change of a function over a specified interval is the ratio: \ $$ \frac{	ext { Change in Output }}{	ext { Change in Input }} $$. \ $$ \square $$ The Average Rate of Change is another term for Slope over a given interval. \ $$ \square $$ If the Average Rate of Change is the same between any two point of a function, then the function \ is Linear Function and the Average Rate of Change equals the Slope. \ $$ \square $$ Average Rate of Changeh $$ \frac{x_{2}-x_{1}}{y_{2}-y_{1}}=\frac{	ext { Change in } \mathrm{x}}{	ext { Change in } y}=\frac{\Delta x}{\Delta y} $$ \ $$ \square $$\end{tabular}

UpStudy AI · Accepted Answer

1. The Average Rate of Change is defined as  
   $$
   \frac{\Delta y}{\Delta x}=\frac{\text{Change in Output}}{\text{Change in Input}}
   $$  
   This verifies the first statement as true.

2. The concept of Slope for a linear function is the same as its Average Rate of Change over any interval. Hence, the second statement is true.

3. For a function, if the Average Rate of Change between any two points is constant, the function is linear and the constant rate is its slope. Thus, the third statement is true.

4. The fourth statement provides  
   $$
   \frac{x_{2}-x_{1}}{y_{2}-y_{1}}=\frac{\Delta x}{\Delta y}
   $$  
   which incorrectly inverts the ratio. The correct formula is  
   $$
   \frac{\Delta y}{\Delta x}=\frac{y_{2}-y_{1}}{x_{2}-x_{1}}.
   $$  
   Therefore, the fourth statement is false.

The true statements are the first, second, and third statements.
The first, second, and third statements are true.

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