91Ó°ÊÓ

Use the analyric method of Example 3 to determine whether the graph of the given function is symmetric with respect to the \(y\) -axis, symmetric with respect to the origin, or neither. Use \(a\) calculator and the standand window to support your conclusion. $$f(x)=0.5 x^{4}-2 x^{2}+1$$

Let the domain of \(f(x)\) be [-1,2] and the range be \([0,3] .\) Find the domain and range of the following. $$f(-3 x)$$

Determine the difference quotient \(\frac{f(x+h)-f(x)}{h}\) (where \(h \neq 0\) j for each function \(f\). Simplify completely. $$f(x)=x^{3}$$

An equation of the form \(|f(x)|=|g(x)|\) is given. (a) Solve the equation analytically and support the solution graphically. (b) Solve \(|f(x)|>|g(x)|\). (c) Solve \(|f(x)|<|g(x)|\). $$|3 x+1|=|2 x-7|$$

Determine the difference quotient \(\frac{f(x+h)-f(x)}{h}\) (where \(h \neq 0\) j for each function \(f\). Simplify completely. $$f(x)=-2 x^{3}$$

An equation of the form \(|f(x)|=|g(x)|\) is given. (a) Solve the equation analytically and support the solution graphically. (b) Solve \(|f(x)|>|g(x)|\). (c) Solve \(|f(x)|<|g(x)|\). $$|x-4|=|7 x+12|$$

Use the analyric method of Example 3 to determine whether the graph of the given function is symmetric with respect to the \(y\) -axis, symmetric with respect to the origin, or neither. Use \(a\) calculator and the standand window to support your conclusion. $$f(x)=0.75 x^{2}+|x|+1$$

each function has a graph with an endpoint (a translation of the point (0,0) .) Enter each into your calculator in an appropriate viewing window, and, using your knowledge of the graph of \(y=\sqrt{x}\), determine the domain and range of the function. (Hint: Locate the endpoint.) $$y=10 \sqrt{x-20}+5$$

Determine the difference quotient \(\frac{f(x+h)-f(x)}{h}\) (where \(h \neq 0\) j for each function \(f\). Simplify completely. $$f(x)=1-x^{2}$$

An equation of the form \(|f(x)|=|g(x)|\) is given. (a) Solve the equation analytically and support the solution graphically. (b) Solve \(|f(x)|>|g(x)|\). (c) Solve \(|f(x)|<|g(x)|\). $$|-2 x+5|=|x+3|$$