91Ó°ÊÓ

Finding the Coordinates of a Point In Exercises 7 and 8 , find the coordinates of the point. The point is located three units to the left of the \(y\) -axis and four units above the \(x\) -axis.

Determining Quadrant(s) for a Point, determine the quadrant(s) in which \((x, y)\) is located so that the condition(s) is (are) satisfied. $$ x=-4 \text { and } y>0 $$

Complete the table. Use the resulting solution points to sketch the graph of the equation. \(y=5-x^{2}\)

Direct Variation In Exercises \(19-26,\) assume that \(y\) is directly proportional to \(x .\) Use the given \(x\) -value and \(y\) -value to find a linear model that relates \(y\) and \(x .\) $$x=4, y=8 \pi$$

Verifying a Polygon, show that the points form the vertices of the indicated polygon. Right triangle: \((4,0),(2,1),(-1,-5)\)

Verifying a Polygon, show that the points form the vertices of the indicated polygon. Right triangle: \((-1,3),(3,5),(5,1)\)

Evaluating a Function In Exercises \(21-32\) , evaluate (if possible) the function at each specified value of the independent variable and simplify. $$ f(x)=\left\\{\begin{array}{ll}{4-5 x,} & {x \leq-2} \\ {0,} & {-2 < x < 2} \\\ {x^{2}+1,} & {x \geq 2}\end{array}\right. $$ $$ \begin{array}{ll}{\text { (a) } f(-3)} & {\text { (b) } f(4)}\end{array} \quad(\text { c) } f(-1) $$

Identifying a Parent Function In Exercises \(21-46\) , \(g\) is related to one of the parent functions described in Section 1.6 (a) Identify the parent function \(f\) . (b) Describe the sequence of transformations from \(f\) to \(g\) . (c) Sketch the graph of \(g\) (d) Use function notation to write \(g\) in terms of $$g(x)=-|x|-2$$

True or False? Determine whether the statement is true or false. Justify your answer. $$\begin{array}{l}{\text { A linear equation will always have an } x \text { -intercept and a }} \\ {y \text { -intercept. }}\end{array}$$

Make a Conjecture Plot the points \((2,1),(-3,5),\) and \((7,-3)\) on a rectangular coordinate system. Then change the signs of the indicated coordinates of each point and plot the three new points on the same rectangular coordinate system. Make a conjecture about the location of a point when each of the following occurs. (a) The sign of the \(x\) -coordinate is changed. (b) The sign of the \(y\) -coordinate is changed. (c) The signs of both the \(x\) - and \(y\) -coordinates are changed.