91Ó°ÊÓ

Determine algebraically whether each function is even, odd, or neither. \(f(x)=x+|x|\)

Find the following for each function: (a) \(f(0)\) (b) \(f(1)\) (c) \(f(-1)\) (d) \(f(-x)\) (e) \(-f(x)\) (f) \(f(x+1)\) (g) \(f(2 x)\) (h) \(f(x+h)\) \(f(x)=3 x^{2}+2 x-4\)

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. $$ f(x)=(x+2)^{3}-3 $$

Determine algebraically whether each function is even, odd, or neither. \(f(x)=\sqrt[3]{2 x^{2}+1}\)

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. $$ g(x)=4 \sqrt{x} $$

Find the following for each function: (a) \(f(0)\) (b) \(f(1)\) (c) \(f(-1)\) (d) \(f(-x)\) (e) \(-f(x)\) (f) \(f(x+1)\) (g) \(f(2 x)\) (h) \(f(x+h)\) \(f(x)=\frac{x}{x^{2}+1}\)

Determine algebraically whether each function is even, odd, or neither. \(g(x)=\frac{1}{x^{2}+8}\)

Determine algebraically whether each function is even, odd, or neither. \(h(x)=\frac{x}{x^{2}-1}\)

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. $$ g(x)=\frac{1}{2} \sqrt{x} $$

Find the following for each function: (a) \(f(0)\) (b) \(f(1)\) (c) \(f(-1)\) (d) \(f(-x)\) (e) \(-f(x)\) (f) \(f(x+1)\) (g) \(f(2 x)\) (h) \(f(x+h)\) \(f(x)=\frac{x^{2}-1}{x+4}\)