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What is the average rate of change of #g(x)=2x-3# between the points (-2,-7) and (3,3)?

Answer 1

Isaiah Allen

It is the same as the slope of the line through those points.

Using the definition #(Delta y)/(Delta x) = (y_2-y_1)/(x_2-x_1) = (3-(-7))/(3-(-2)) = 10/5 = 2#

Making use of past knowledge

The two points line on a line that has slope #2# so the slope of the line through the two points is #2#

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Answer 2

Elijah Abram

To find the average rate of change of the function ( g(x) = 2x - 3 ) between the points ((-2, -7)) and ((3, 3)), you use the formula:

[ \text{Average Rate of Change} = \frac{\text{Change in Output}}{\text{Change in Input}} ]

[ \text{Average Rate of Change} = \frac{g(3) - g(-2)}{3 - (-2)} ]

[ \text{Average Rate of Change} = \frac{(2 \times 3 - 3) - (2 \times (-2) - 3)}{3 - (-2)} ]

[ \text{Average Rate of Change} = \frac{(6 - 3) - (-4 - 3)}{3 + 2} ]

[ \text{Average Rate of Change} = \frac{3 - (-7)}{5} ]

[ \text{Average Rate of Change} = \frac{10}{5} ]

[ \text{Average Rate of Change} = 2 ]

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Answer from HIX Tutor

When evaluating a one-sided limit, you need to be careful when a quantity is approaching zero since its sign is different depending on which way it is approaching zero from. Let us look at some examples.