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Chapter 2: Problem 53
Find the domain of each function. $$g(x)=\frac{3}{x-4}$$
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Begin by graphing the standard quadratic function, \(f(x)=x^{2} .\) Then use transformations of this graph to graph the given function. $$ g(x)=2(x-2)^{2} $$
Begin by graphing the square root function, \(f(x)=\sqrt{x} .\) Then use transformations of this graph to graph the given function. $$ h(x)=\sqrt{x+1}-1 $$
Begin by graphing the standard cubic function, \(f(x)=x^{3} .\) Then use transformations of this graph to graph the given function. $$ h(x)=\frac{1}{2} x^{3} $$
You will be developing functions that model given conditions. Describe one advantage of using \(f(x)\) rather than \(y\) in a function's equation.
Which one of the following is true? a. If \(f(x)=|x|\) and \(g(x)=|x+3|+3,\) then the graph of \(g\) is a translation of three units to the right and three units upward of the graph of \(f\) b. If \(f(x)=-\sqrt{x}\) and \(g(x)=\sqrt{-x},\) then \(f\) and \(g\) have identical graphs. c. If \(f(x)=x^{2}\) and \(g(x)=5\left(x^{2}-2\right),\) then the graph of \(g\) can be obtained from the graph of \(f\) by stretching \(f\) five units followed by a downward shift of two units. d. If \(f(x)=x^{3}\) and \(g(x)=-(x-3)^{3}-4,\) then the graph of \(g\) can be obtained from the graph of \(f\) by moving \(f\) three units to the right, reflecting in the \(x\) -axis, and then moving the resulting graph down four units.
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