91Ó°ÊÓ

In Exercises \(53-64,\) complete the square and write the equation in standard form. Then give the center and radius of each circle and graph the equation. $$x^{2}+y^{2}+8 x+4 y+16=0$$

Begin by graphing the standard quadratic function, \(f(x)=x^{2} .\) Then use transformations of this graph to graph the given function. $$g(x)=x^{2}-1$$

graph each equation in a rectangular coordinate system. $$x=0$$

Find a. \((f \circ g)(x)\) b. \((g \circ f)(x)\) c. \((f \circ g)(2)\) d. \((g \circ f)(2)\) $$f(x)=4 x-3, g(x)=5 x^{2}-2$$

In Exercises \(53-64,\) complete the square and write the equation in standard form. Then give the center and radius of each circle and graph the equation. $$x^{2}+y^{2}-10 x-6 y-30=0$$

graph each equation in a rectangular coordinate system. $$f(x)=1$$

Begin by graphing the standard quadratic function, \(f(x)=x^{2} .\) Then use transformations of this graph to graph the given function. $$g(x)=(x-2)^{2}$$

Evaluate each piecewise function at the given values of the independent variable. \(g(x)=\left\\{\begin{array}{ll}x+3 & \text { if } \quad x \geq-3 \\ -(x+3) & \text { if } \quad x<-3\end{array}\right.\) a. \(g(0)\) b. \(g(-6)\) c. \(g(-3)\)

Evaluate each piecewise function at the given values of the independent variable. \(g(x)=\left\\{\begin{array}{ll}x+5 & \text { if } x \geq-5 \\ -(x+5) & \text { if } x<-5\end{array}\right.\) a. \(g(0)\) b. \(g(-6)\) c. \(g(-5)\)

Begin by graphing the standard quadratic function, \(f(x)=x^{2} .\) Then use transformations of this graph to graph the given function. $$g(x)=(x-1)^{2}$$