Question

The graph of g is a translation 1 unit down of the graph of f(x) = 3|x| – 4. The rate of change of g over the interval 2 ≤ x ≤ 5 is; (choose): 1,2,3,4

Answer 1

Since the graph of f(x) is translated 1 unit down, we need to decrease the value of f(x) by 1 to find g(x):

`\begin{gathered} g(x)=f(x)-1\\ \\ g(x)=3|x|-4-1\\ \\ g(x)=3|x|-5 \end{gathered}`

Now, to calculate the rate of change over the interval 2 <= x <= 5, we can use the formula below:

`\begin{gathered} rate=(g(5)-g(2))/(5-2)\\ \\ g(5)=3\cdot5-5=10\\ \\ g(2)=3\cdot2-5=1\\ \\ rate=(10-1)/(3)=(9)/(3)=3 \end{gathered}`

Therefore the rate of change is 3.