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Average rate of change worksheets Grade 10

Find the average rate of change of a function between two x values.

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How to do it

The average rate of change from x = a to x = b is (f(b) − f(a)) ÷ (b − a).

f(x)=−2x2−x−4;from −2 to 4→−5f(x) = -2x^{2} - x - 4;\quad \text{from }-2\ \text{to }4\quad \to \quad -5
f(4)=−2(4)2−(4)−4=−40f(4) = -2(4)^{2} - (4) - 4 = -40
f(−2)=−2(−2)2−(−2)−4=−10f(-2) = -2(-2)^{2} - (-2) - 4 = -10
−40−(−10)4−(−2)=−306=−5\dfrac{-40 - (-10)}{4 - (-2)} = \dfrac{-30}{6} = -5the change in f over the change in x

Example problems

  1. f(x)=−3x2+6;from 1 to 2→f(x) = -3x^{2} + 6;\quad \text{from }1\ \text{to }2\quad \to \quad
  2. f(x)=−3x2+x+1;from 3 to 5→f(x) = -3x^{2} + x + 1;\quad \text{from }3\ \text{to }5\quad \to \quad
  3. f(x)=x3+2x−4;from 3 to 4→f(x) = x^{3} + 2x - 4;\quad \text{from }3\ \text{to }4\quad \to \quad
  4. f(x)=x3+2x+1;from −1 to 1→f(x) = x^{3} + 2x + 1;\quad \text{from }-1\ \text{to }1\quad \to \quad

Functions

  1. Evaluating functions
  2. Finding the domain of a function
  3. Adding, subtracting and multiplying functions
  4. Composition of functions
  5. Inverse functions
  6. Transformations of functions
  7. Even and odd functions
  8. Average rate of change