Rate of Change (Algebraic) Math Example 4

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Example 4

hard
Find the average rate of change of g(x)=2x2−3g(x) = 2x^2 - 3 from x=−1x = -1 to x=3x = 3.

Solution

  1. 1
    g(−1)=2(1)−3=−1g(-1) = 2(1) - 3 = -1; g(3)=2(9)−3=15g(3) = 2(9) - 3 = 15.
  2. 2
    Rate = 15−(−1)3−(−1)=164=4\frac{15 - (-1)}{3 - (-1)} = \frac{16}{4} = 4.

Answer

44
Be careful with negative inputs: (−1)2=1(-1)^2 = 1, and the denominator includes the full distance between xx-values.

About Rate of Change (Algebraic)

The ratio of how much one quantity changes to how much another quantity changes — measured over an interval.

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More Rate of Change (Algebraic) Examples

Example 1 easy

A car travels 150 miles in 3 hours. What is its average rate of change (speed)?

Example 2 medium

Find the average rate of change of [formula] from [formula] to [formula].

Example 3 easy

A plant grows from 5 cm to 17 cm in 4 weeks. What is the average growth rate?

← All Rate of Change (Algebraic) Examples Rate of Change (Algebraic) Concept

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