which function on this graph (linear, quadratic, or exponential) will have the largest average rate of…

which function on this graph (linear, quadratic, or exponential) will have the largest average rate of change when x is large? which will have the smallest? rank the functions in increasing order of long - term average rate of change. text description for graph a. exponential, quadratic, linear b. linear, exponential, quadratic c. quadratic, linear, exponential d. linear, quadratic, exponential

which function on this graph (linear, quadratic, or exponential) will have the largest average rate of change when x is large? which will have the smallest? rank the functions in increasing order of long - term average rate of change. text description for graph a. exponential, quadratic, linear b. linear, exponential, quadratic c. quadratic, linear, exponential d. linear, quadratic, exponential

Answer

Explanation:

Step1: Recall rate - of - change properties

The average rate of change of a linear function $y = mx + b$ is a constant $m$. A quadratic function $y=ax^{2}+bx + c$ has an average rate of change that grows linearly as $x$ increases. An exponential function $y = a\cdot b^{x}(b>1)$ has an average rate of change that grows exponentially as $x$ increases.

Step2: Compare long - term growth

As $x$ gets large, the exponential function will have the largest average rate of change. The linear function has a constant average rate of change, and the quadratic function has a growing but slower - than - exponential average rate of change. So, in increasing order of long - term average rate of change, the order is linear, quadratic, exponential.

Answer:

D. Linear, quadratic, exponential