Question

question 13 (5 points)
find the average rate of change of ( f(x)=sqrt{x + 6} ) on (4,9). round your answer to the nearest hundredth.
0.14
0.71
-0.36
-0.14
question 14 (5 points)
state whether the graph of ( -\frac{4}{x^{2}} ) has infinite discontinuity, jump discontinuity, point discontinuity, or is continuous.
the function is continuous.
the function has infinite discontinuity.
the function has point discontinuity.
the function has jump discontinuity.

Explanation:

Step1: Recall the formula for average rate of change

The average rate of change of a function \(y = f(x)\) on the interval \([a,b]\) is given by \(\frac{f(b)-f(a)}{b - a}\). Here, \(a = 4\), \(b=9\), and \(f(x)=\sqrt{x + 6}\).

Step2: Calculate \(f(4)\) and \(f(9)\)

• For \(x = 4\), \(f(4)=\sqrt{4+6}=\sqrt{10}\approx3.16\)
• For \(x = 9\), \(f(9)=\sqrt{9 + 6}=\sqrt{15}\approx3.87\)

Step3: Substitute into the average - rate - of - change formula

\(\frac{f(9)-f(4)}{9 - 4}=\frac{\sqrt{15}-\sqrt{10}}{5}\approx\frac{3.87-3.16}{5}=\frac{0.71}{5}=0.14\)

Answer:

0.14