91Ó°ÊÓ

Determine whether each point lies on the graph of the equation. \(y=\frac{1}{3} x^{3}-2 x^{2}\) (a) \(\left(2,-\frac{16}{3}\right) \quad\) (b) \((-3,9)\)

Testing for Functions Represented Algebraically In Exercises \(11-20\) , determine whether the equation represents \(y\) as a function of \(x .\) $$(x-2)^{2}+y^{2}=4$$

Evaluating an Arithmetic Combination of Functions In, evaluate the indicated function for \(f(x)=x^{2}+1\) and \(g(x)=x-4\) . $$(f-g)(-1)$$

Writing a Linear Function. (a) write the linear function \(f\) such that it has the indicated function values and (b) sketch the graph of the function. $$f\left(\frac{2}{3}\right)=-\frac{15}{2}, \quad f(-4)=-11$$

find the zeros of the function algebraically. \(f(x)=2 x^{2}-7 x-30\)

Graphing a Linear Equation find the slope and \(y\) -intercept (if possible) of the equation of the line. Sketch the line. $$y=5 x+3$$

Evaluating an Arithmetic Combination of Functions In, evaluate the indicated function for \(f(x)=x^{2}+1\) and \(g(x)=x-4\) . $$(f-g)(0)$$

Complete the table. Use the resulting solution points to sketch the graph of the equation. \(y=-2 x+5\)

Graphing a Function. Use a graphing utility to graph the function. Be sure to choose an appropriate viewing window. $$f(x)=2.5 x-4.25$$

Testing for Functions Represented Algebraically In Exercises \(11-20\) , determine whether the equation represents \(y\) as a function of \(x .\) $$y=\sqrt{16-x^{2}}$$