91Ó°ÊÓ

In \(12-23,\) each set is a function from set \(A\) to set \(B .\) a. What is the largest subset of the real numbers that can be set \(A\) , the domain of the given function? b. If set \(A=\operatorname{set} B,\) is the function onto? Justify your answer. $$ \left\\{(x, y) : y=\frac{1}{\sqrt{x+1}}\right\\} $$

In \(20-27\) : a. Write each equation in center-radius form. b. Find the coordinates of the center. . Find the radius of the circle. $$ x^{2}+y^{2}-25=0 $$

\(\operatorname{In} 19-22,\) let \(\mathrm{f}(x)=|x| \cdot\) Find \(\mathrm{f}(\mathrm{g}(x))\) and \(\mathrm{g}(\mathrm{f}(x))\) for each given function. $$ g(x)=2 x+3 $$

a. Sketch the graph of \(y=x^{2} .\) b. Sketch the graph of \(y=x^{2}+2\) c. Sketch the graph of \(y=x^{2}-3\) d. Describe the graph of \(y=x^{2}+a\) in terms of the graph of \(y=x^{2}\) . e. What transformation maps \(y=x^{2}\) to \(y=x^{2}+a ?\)

In \(20-27\) : a. Write each equation in center-radius form. b. Find the coordinates of the center. . Find the radius of the circle. $$ x^{2}+y^{2}-2 x-2 y-7=0 $$

If \(\mathrm{f}=\\{(x, y) : y=5 x\\}\) is a direct variation function, find \(\mathrm{f}^{-1}\)

Is every linear function a direct variation?

In \(12-23,\) each set is a function from set \(A\) to set \(B .\) a. What is the largest subset of the real numbers that can be set \(A\) , the domain of the given function? b. If set \(A=\operatorname{set} B,\) is the function onto? Justify your answer. $$ \left\\{(x, y) : y=\frac{1}{x^{2}+1}\right\\} $$

If \(\mathrm{g}=\\{(x, y) : y=7-x\\},\) find \(\mathrm{g}^{-1}\) if it exists. Is it possible for a function to be its own inverse?

Is the direct variation of two variables always a linear function?