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Which of the following functions has a rate of change that is less than the rate of change of the linear function represented by the table of values below?

A) A quadratic function
B) A linear function with a steeper slope
C) An exponential function
D) Another linear function with a shallower slope

User Xxg
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Final answer:

The function with a rate of change that is less than the given linear function is another linear function with a shallower slope, meaning it has a lower slope and hence a lower rate of change.

Step-by-step explanation:

The student has asked which function has a rate of change that is less than the rate of change of a given linear function. To answer this, we must understand what 'rate of change' refers to in different types of functions. The rate of change for a linear function is its slope. For a quadratic function, the rate of change varies and is not constant, as it is for a linear function, but on average, it could be higher or lower than that of a particular linear function. An exponential function typically increases or decreases at a rate that becomes increasingly steep, so its rate of change generally exceeds that of a linear function over time. Therefore, the correct answer would be D) Another linear function with a shallower slope, as 'shallower slope' literally means a lower rate of change compared to a steeper linear function.

User Nicholas Blasgen
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