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. $$x^{2}+y^{2}+3 x+5 y+\frac{9}{4}=0$$

Explain how to graph an equation in the rectangular coordinate system.

The domain of each piecewise function \(i s(-\infty, \infty)\). a. Graph each function. b. Use your graph to determine the function's range. $$f(x)=\left\\{\begin{array}{lll}x+2 & \text { if } & x<-3 \\\x-2 & \text { if } & x \geq-3\end{array}\right.$$

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

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

What does a \([-20,2,1]\) by \([-4,5,0.5]\) viewing rectangle mean?

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. $$3 y-9=0$$

The domain of each piecewise function \(i s(-\infty, \infty)\). a. Graph each function. b. Use your graph to determine the function's range. $$f(x)=\left\\{\begin{array}{rll}3 & \text { if } & x \leq-1 \\\\-3 & \text { if } & x>-1\end{array}\right.$$

The figure shows a Norman window that has the shape of a rectangle with a semicircle attached at the top. The diameter of the semicircle is equal to the width of the rectangle. The window has a perimeter of 12 feet. Express the area of the window, \(A\), as a function of its radius, \(r\).

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. $$4 y+28=0$$