Questions: Introduction to Exponential Functions If the Inputs change at a constant rate, which of the following are true of Linear and Exponential Functions? Check all that apply. The outputs for Exponential Functions change by Addition. The outputs for Linear Functions change by Addition. The outputs for Linear Functions change by Multiplication. The outputs for Exponential Functions change by Multiplication.

Solution Steps

To determine the characteristics of Linear and Exponential Functions, we need to understand how their outputs change with respect to their inputs. For Linear Functions, the outputs change by a constant addition, meaning they have a constant rate of change. For Exponential Functions, the outputs change by a constant multiplication, meaning they grow by a constant factor.

For Linear Functions, the outputs change by a constant addition. This means that if we have a function \( f(x) = mx + b \), the change in output for a change in input \( \Delta x \) is given by \( \Delta f = m \Delta x \). Thus, the statement "The outputs for Linear Functions change by Addition" is true.

For Exponential Functions, the outputs change by a constant multiplication. This can be represented as \( f(x) = a \cdot b^x \), where \( b \) is a constant greater than 1. The change in output for a change in input \( \Delta x \) is given by \( \Delta f = a \cdot b^{x + \Delta x} - a \cdot b^x = a \cdot b^x (b^{\Delta x} - 1) \). Therefore, the statement "The outputs for Exponential Functions change by Multiplication" is true.

Based on the analysis:

• "The outputs for Exponential Functions change by Addition." is false.
• "The outputs for Linear Functions change by Addition." is true.
• "The outputs for Linear Functions change by Multiplication." is false.
• "The outputs for Exponential Functions change by Multiplication." is true.

Final Answer