91Ó°ÊÓ

Find an equation of variation for the given situation. \(y\) varies jointly as \(x\) and \(z,\) and \(y=56\) when \(x=7\) and \(z=8\).

Describe how the graph of the function can be obtained from one of the basic graphs on \(p\). 129 $$g(x)=\left|\frac{1}{3} x\right|-4$$

Use a graphing calculator to find the intervals on which the function is increasing or decreasing. Consider the entire set of real numbers if no domain is given. $$f(x)=\frac{8 x}{x^{2}+1}$$

Find the point that is symmetric to the given point with respect to the \(x\) -axis, the \(y\) -axis, and the origin. $$(-10,-7)$$

Find the point that is symmetric to the given point with respect to the \(x\) -axis, the \(y\) -axis, and the origin. $$\left(1, \frac{3}{8}\right)$$

Describe how the graph of the function can be obtained from one of the basic graphs on \(p\). 129 $$f(x)=\frac{2}{3} x^{3}-4$$

Find \((f \circ g)(x)\) and \((g \circ f)(x)\) and the domain of each. $$f(x)=x^{4}, g(x)=\sqrt[4]{x}$$

Use a graphing calculator to find the intervals on which the function is increasing or decreasing. Consider the entire set of real numbers if no domain is given. $$f(x)=\frac{-4}{x^{2}+1}$$

For each pair of functions in Exercises \(17-34\) : A. Find the domain of \(f, g, f+g, f-g, f g, f f, f / g\) and \(g / f\) B. Find \((f+g)(x),(f-g)(x),(f g)(x),(f f)(x)\) \((f / g)(x),\) and \((g / f)(x)\) $$f(x)=2 x^{2}, g(x)=\frac{2}{x-5}$$

Find an equation of variation for the given situation. \(y\) varies directly as \(x\) and inversely as \(z,\) and \(y=4\) when \(x=12\) and \(z=15\).