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. $$x^{2}+y^{2}+12 x-6 y-4=0$$

graph each equation in a rectangular coordinate system. $$3 x+12=0$$

Find a. \((f \circ g)(x)\) b. \((g \circ f)(x)\) c. \((f \circ g)(2)\) d. \((g \circ f)(2)\) $$f(x)=x^{2}+1, g(x)=x^{2}-3$$

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. $$x^{2}-2 x+y^{2}-15=0$$

The function \(f(x)=30 x+0.08\) is a reasonable model for the monthly cost, \(f\), in dollars, for a text message plan in terms of the number of monthly text messages, \(x .\)

a. Rewrite the given equation in slope-intercept form. b. Give the slope and y-intercept. c. Use the slope and y-intercept to graph the linear function. $$3 x+y-5=0$$

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

Let $$\begin{array}{l} f(x)=2 x-5 \\ g(x)=4 x-1 \\ h(x)=x^{2}+x+2 \end{array}$$ Evaluate the indicated function without finding an equation for the function. $$(f \circ g)(0)$$

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

The domain of each piecewise function \(i s(-\infty, \infty)\). a. Graph each function. b. Use your graph to determine the function's range. $$f(x)=\left\\{\begin{array}{rll}-x & \text { if } & x<0 \\\x & \text { if } & x \geq 0\end{array}\right.$$