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

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30-10-2022
Mathematics

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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

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AnnaliciaW716395 AnnaliciaW716395 · Answer 1 · 2022-10-30T15:01:25+01:00

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):

[tex]\begin{gathered} g(x)=f(x)-1\\ \\ g(x)=3|x|-4-1\\ \\ g(x)=3|x|-5 \end{gathered}[/tex]

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

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

Therefore the rate of change is 3.