91Ó°ÊÓ

Sketch the curve by eliminating the parameter, and indicate the direction of increasing \(t\). $$x=\sec ^{2} t, \quad y=\tan ^{2} t$$

Generate the graph of \(f\) in a viewing window that you think is appropriate. $$f(x)=12 \sin (x / 80)$$

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. $$y=3-\sqrt{x+1}$$

Generate the graph of \(f\) in a viewing window that you think is appropriate. $$f(x)=300-10 x^{2}+0.01 x^{3}$$

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) \(y=-x^{n}\) (b) \(y=2 x^{-n}\) (c) \(y=(x-1)^{1 / n}\)

Find parametric equations for the curve, and check your work by generating the curve with a graphing utility A circle of radius \(5,\) centered at the origin, oriented clockwise.

Express the function in piecewise form without using absolute values. [Suggestion: It may help to generate the graph of the function.] (a) \(f(x)=|x|+3 x+1\) (b) \(g(x)=|x|+|x-1|\)

Find the angle of inclination of the line to the nearest degree. Use a calculating utility, where needed. (a) \(y=\sqrt{3} x+2\) (b) \(y+2 x+5=0\)

Generate the graph of \(f\) in a viewing window that you think is appropriate. $$f(x)=x(30-2 x)(25-2 x)$$

Express the function in piecewise form without using absolute values. [Suggestion: It may help to generate the graph of the function.] (a) \(f(x)=3+|2 x-5|\) (b) \(g(x)=3|x-2|-|x+1|\)