Question

The graph of g is a translation 4 unit down of the graph of f(x) = 6x-4. The rate of change of g over the interval -2 ≤ x ≤ 4 is

Answer 1

The function g(x) is a linear function, and the rate of change over the interval  -2 ≤ x ≤ 4 is 6

How to determine the rate of change?

The function f is given as:

f(x) =6x - 4

When translated down by 6 units, the rule of translation is:

g(x) = f(x) - 4

So, we have:

g(x) = 6x - 4 - 4

Evaluate

g(x) = 6x - 8

The rate of change over -2 ≤ x ≤ 4 is then calculated using:

g'(x) = [g(b) - g(a)]/[b - a]

So, we have:

g'(x) = [g(4) - g(-2)]/[4 + 2]

Evaluate

g'(x) = [g(4) - g(-2)]/[6]

Calculate g(4) and g(-2)

g(4) = 6 * 4 - 8 = 16

g(-2) = 6 * -2 - 8 = -20

So, we have:

g'(x) = (16 + 20)/6

Evaluate

g'(x) = 6

Hence, the rate of change over the interval  -2 ≤ x ≤ 4 is 6

Read more about rate of change at:

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