91Ó°ÊÓ

Decide whether or not each equation has a circle as its graph. If it does, give the center and the radius. If it does not, describe the graph. $$x^{2}+y^{2}+8 x-6 y+16=0$$

Fill in each blank with the appropriate response: The line \(x+2=0\) has \(x\) -intercept _______. It _______ have a y-intercept. The slope of this line is ______ (O/undefined) The line \(4 y=2\) has \(y\) -intercept _______. It_________ (does/does not) have an \(x\) -intercept. The slope of this line is _______ (0/undefined).

Decide whether each relation defines \(y\) as a function of \(x\). Give the domain and range. $$y=-6 x+4$$

Plot each point, and then plot the points that are symmetric to the given point with respect to the ( \(a\) ) \(x\) -axis, (b) y-axis, and (c) origin. $$(5,-3)$$

Plot each point, and then plot the points that are symmetric to the given point with respect to the ( \(a\) ) \(x\) -axis, (b) y-axis, and (c) origin. $$(-4,-2)$$

Without graphing, determine whether each equation has a graph that is symmetric with respect to the \(x\) -axis, the \(y\) -axis, the origin, or none of these. $$y=x^{2}+5$$

Find the center-radius form of the circle described or graphed. a circle having a diameter with endpoints \((-1,2)\) and \((11,7)\)

Choose the correct answer: For function \(f,\) the notation \(f(3)\) means A. the variable \(f\) times \(3,\) or \(3 f\). B. the value of the dependent variable when the independent variable is 3 . C. the value of the independent variable when the dependent variable is 3 . D. \(f\) equals 3.

Write the distance formula \(d=\sqrt{\left(x_{2}-x_{1}\right)^{2}+\left(y_{2}-y_{1}\right)^{2}}\) using a rational exponent.

Solve each problem. To visualize the situation, use graph paper and a pair of compasses to carefully draw the graphs of the circles. Suppose that receiving stations \(P, Q,\) and \(R\) are located on a coordinate plane at the points \((3,1),(5,-4),\) and \((-1,4),\) respectively. The epicenter of an earthquake is determined to be \(\sqrt{5}\) units from \(P, 6\) units from \(Q,\) and \(2 \sqrt{10}\) units from \(R .\) Where on the coordinate plane is the epicenter located?