91Ó°ÊÓ

Find equations for the \(x\) - and \(y\) -axes.

Sketch the graph of the equation by translating, reflecting, compressing, and stretching the graph of \(y=\sqrt{x}\) appropriately, and then use a graphing utility to confirm that your sketch is correct. $$y=1+\sqrt{x-4}$$

Sketch the graph of the equation for \(n=1,3,\) and 5 in one coordinate system and for \(n=2,4\) and 6 in another coordinate system. Check your work with a graphing utility. (a) \(y=2 x^{n}\) (b) \(y=-x^{-n}\) (c) \(y=-3(x+2)^{1 / n}\)

Find parametric equations for the curve, and check your work by generating the curve with a graphing utility The portion of the circle \(x^{2}+y^{2}=1\) that lies in the third quadrant, oriented counterclockwise.

Generate the graph of \(f\) in a viewing window that you think is appropriate. $$f(x)=x^{2}+\frac{1}{x}$$

(a) Sketch the graph of \(y=a x^{2}\) for \(a=\pm 1,\pm 2,\) and ±3 in a single coordinate system. (b) Sketch the graph of \(y=x^{2}+b\) for \(b=\pm 1,\pm 2,\) and ±3 in a single coordinate system. (c) Sketch some typical members of the family of curves \(y=a x^{2}+b\)

Find parametric equations for the curve, and check your work by generating the curve with a graphing utility A vertical line intersecting the \(x\) -axis at \(x=2,\) oriented upward.

Find the slope-intercept form of the equation of the line satisfying the stated conditions, and check your answer using a graphing utility. Slope \(=-2, y\) -intercept \(=4\)

Sketch the graph of the equation by translating, reflecting, compressing, and stretching the graph of \(y=\sqrt{x}\) appropriately, and then use a graphing utility to confirm that your sketch is correct. $$y=\frac{1}{2} \sqrt{x}+1$$

Sketch the graph of the equation by translating, reflecting, compressing, and stretching the graph of \(y=\sqrt{x}\) appropriately, and then use a graphing utility to confirm that your sketch is correct. $$y=-\sqrt{3 x}$$