5. Let \(f(x)=\sqrt[3]{x}\), and \(g(x)=x-4\). Find each of the following.

a) \((f+g)(8)\)

b) \((f-g)(x)\)

c) \((fg)(27)\)

d) \(\left(\frac{f}{g} ight)(x)\)

6. If a comedian drops a watermelon from a height of \(64 ft\) then its height (in feet) above the ground is given by the function \(h(t)=-16t^{2}+64\), where \(t\) is the time (in seconds). To get an idea of how fast the watermelon is traveling when it hits the ground, find the average rate of change of the height of the watermelon over the given time intervals.

a) \([0,2]\)

b) \([1,2]\)

c) \([1.92, 2]\)

d) \([1.99,2]\)

e. \([1.999,2]\)

7. Write the equation of each graph after the indicated transformation(s).

a). The graph of \(y=x^2\) is translated five units to the right.

b) The graph of \(y=\sqrt{x}\) is translated five units to the left and twelve units downward.

c) The graph of \(y=|x|\) is reflected in the x - axis, stretched by a factor of 3, then translated seven units to the right and nine units upward.

8. Determine algebraically whether the function is even, odd, or neither. Discuss the symmetry of each function.

a) \(f(x)=x^{4}-2x^{2}\)

b) \(f(x)=x^{3}-x\)

c) \(f(x)=|x|-9\)

d) \(f(x)=x^3-5x+1\)