91Ó°ÊÓ

sketch the graph of each function. Do not use a graphing calculator. (Assume the largest possible domain.) $$ y=-2 \cos (\pi x / 4) $$

Determine the equation of the line that satisfies the stated requirements. Put the equation in standard form. The line with slope \(-1 / 3\) and \(y\) -intercept \((0,1 / 3)\)

Determine the equation of the line that satisfies the stated requirements. Put the equation in standard form. The line with slope \(-2\) and \(x\) -intercept \((1,0)\)

Graph \(y=x^{n}, x \geq 0\), for \(n=1,2,3\), and 4 in one coordinate system. Where do the curves intersect?

Explain how the following functions can be obtained from \(y=x^{2}\) by basic transformations: (a) \(y=x^{2}-2\) (b) \(y=(x-1)^{2}+1\) (c) \(y=-2(x+2)^{2}\)

Determine the equation of the line that satisfies the stated requirements. Put the equation in standard form. The line with slope 1 and \(x\) -intercept ( 2,0 )

Explain how the following functions can be obtained from \(y=x^{3}\) by basic transformations: (a) \(y=x^{3}-1\) (b) \(y=-x^{3}-1\) (c) \(y=-3(x-1)^{3}\)

(a) Graph \(f(x)=x, x \geq 0\), and \(g(x)=x^{2}, x \geq 0\), together, in one coordinate system. (b) For which values of \(x\) is \(f(x) \geq g(x)\), and for which values of \(x\) is \(f(x) \leq g(x)\) ?

(a) Graph \(f(x)=x^{2}\) and \(g(x)=x^{3}\) for \(x \geq 0\), together, in one coordinate system. (b) Show algebraically that \(x \geq x^{2}\) for \(0 \leq x \leq 1\). (c) Show algebraically that \(x \leq x^{2}\) for \(x \geq 1\).

Determine the equation of the line that satisfies the stated requirements. Put the equation in standard form. The line with slope \(-1 / 2\) and \(x\) -intercept \((-1 / 2,0)\)