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Magazine Problem 38
Determine whether the equation defines y as a function of \(x .\) \(x+y^{2}=1\)
Problem 38
Graph each function using the techniques of shifting, compressing, stretching, and/or reflecting. Start with the graph of the basic function (for example, \(y=x^{2}\) ) and show all the steps. Be sure to show at least three key points. Find the domain and the range of each function. $$ f(x)=x^{2}+4 $$
Problem 38
Determine algebraically whether each function is even, odd, or neither. \(f(x)=2 x^{4}-x^{2}\)
Problem 39
Determine algebraically whether each function is even, odd, or neither. \(g(x)=10-x^{2}\)
Problem 39
Determine whether the equation defines y as a function of \(x .\) \(y=\sqrt[3]{x}\)
Problem 39
Graph each function using the techniques of shifting, compressing, stretching, and/or reflecting. Start with the graph of the basic function (for example, \(y=x^{2}\) ) and show all the steps. Be sure to show at least three key points. Find the domain and the range of each function. $$ g(x)=\sqrt{3 x} $$
Problem 40
Determine algebraically whether each function is even, odd, or neither. \(h(x)=3 x^{3}+5\)
Problem 40
Determine whether the equation defines y as a function of \(x .\) \(y=\frac{3 x-1}{x+2}\)
Problem 40
Challenge Problem Suppose \(f(x)=x^{2}-4 x+c\) and \(g(x)=\frac{f(x)}{3}-4 .\) Find \(f(3)\) if \(g(-2)=5\)
Problem 40
Graph each function using the techniques of shifting, compressing, stretching, and/or reflecting. Start with the graph of the basic function (for example, \(y=x^{2}\) ) and show all the steps. Be sure to show at least three key points. Find the domain and the range of each function. $$ g(x)=\sqrt[3] \frac{1}{2} x $$
