91Ó°ÊÓ

Use the algebraic tests to check for symmetry with respect to both axes and the origin. $$ y=\frac{1}{x^{2}+1} $$

The simple interest on an investment is directly proportional to the amount of the investment. By investing \(\$ 3250\) in a certain bond issue, you obtained an interest payment of \(\$ 113.75\) after 1 year. Find a mathematical model that gives the interest \(I\) for this bond issue after 1 year in terms of the amount invested \(P\)

Property tax is based on the assessed value of a property. A house that has an assessed value of \(\$ 150,000\) has a property tax of \(\$ 5520\). Find a mathematical model that gives the amount of property \(\operatorname{tax} y\) in terms of the assessed value \(x\) of the property. Use the model to find the property tax on a house that has an assessed value of \(\$ 225,000\).

\(\mathrm{G}\) is related to one of the parent functions described in Section 1.6. (a) Identify the parent function \(f\). (b) Describe the sequence of transformations from \(f\) to \(g\). (c) Sketch the graph of \(g\). (d) Use function notation to write \(g\) in terms of \(f\). $$ g(x)=-|x+4|+8 $$

Use a graphing utility to graph the function, and use the Horizontal Line Test to determine whether the function is one-to-one and so has an inverse function. $$ g(x)=\frac{4-x}{6} $$

Evaluate the function for the indicated values. \(f(x)=\llbracket x \rrbracket\) (a) \(f(2.1)\) (b) \(f(2.9)\) (c) \(f(-3.1)\) (d) \(f\left(\frac{7}{2}\right)\)

State sales tax is based on retail price. An item that sells for $$\$ 189.99$$ has a sales tax of $$\$ 11.40 .$$ Find a mathematical model that gives the amount of sales tax \(y\) in terms of the retail price \(x .\) Use the model to find the sales tax on a \(\$ 639.99\) purchase.

Show that the points form the vertices of the indicated polygon. Isosceles triangle: (2,3),(4,9),(-2,7)

Find a mathematical model for the verbal statement. A varies directly as the square of \(r\).

Sketch the graph of the function. $$ g(x)=4 \llbracket x \rrbracket $$