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Magazine Problem 82
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 \(|f(x)|<|g(x)|\). $$|-5 x+1|=|3 x-4|$$
Problem 82
Determine the difference quotient \(\frac{f(x+h)-f(x)}{h}\) (where \(h \neq 0\) j for each function \(f\). Simplify completely. $$f(x)=x^{2}+2 x$$
Problem 82
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.) $$y=-2 \sqrt{x+15}-18$$
Problem 83
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 \(|f(x)|<|g(x)|\). $$\left|x-\frac{1}{2}\right|=\left|\frac{1}{2} x-2\right|$$
Problem 83
In Exercises \(81-83 \text { , each function has a graph with an endpoint (a translation of the point }(0,0) .)\) 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.) $$y=-0.5 \sqrt{x+10}+5$$
Problem 83
Determine the difference quotient \(\frac{f(x+h)-f(x)}{h}\) (where \(h \neq 0\) j for each function \(f\). Simplify completely. $$f(x)=3 x^{2}$$
Problem 83
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. $$f(x)=x^{6}-4 x^{3}$$
Problem 84
Determine the difference quotient \(\frac{f(x+h)-f(x)}{h}\) (where \(h \neq 0\) j for each function \(f\). Simplify completely. $$f(x)=\sqrt{x}$$
Problem 84
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. $$f(x)=x^{3}-3 x$$
Problem 84
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 \(|f(x)|<|g(x)|\). $$|x+3|=\left|\frac{1}{3} x+8\right|$$
