Questions: If the inputs are evenly spaced, how do the outputs of linear and exponential functions change? The outputs of exponential functions change by multiplication/division. The outputs of linear functions change by addition/subtraction.

Solution Steps

The question asks how the outputs of linear and exponential functions change when the inputs are evenly spaced. Specifically, it asks whether the outputs change by addition/subtraction or multiplication/division.

For a linear function \( f(x) = mx + b \), where \( m \) is the slope and \( b \) is the y-intercept, the outputs change by a constant amount (addition/subtraction) when the inputs are evenly spaced. This is because the slope \( m \) represents the rate of change, which is constant for linear functions.

For an exponential function \( f(x) = a \cdot b^x \), where \( a \) is the initial value and \( b \) is the base, the outputs change by a constant factor (multiplication/division) when the inputs are evenly spaced. This is because the function grows or decays by a multiplicative factor \( b \) for each unit increase in \( x \).

Final Answer