91Ó°ÊÓ

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

Determine the equation of the line that satisfies the stated requirements. Put the equation in standard form. The line with slope 3 and \(y\) -intercept \((0,2)\)

Suppose that \(f(x)=x^{2}, x \geq 0\), and \(g(x)=\sqrt{x}, x \geq 0\). Typically, \(f \circ g \neq g \circ f\), but this is an example in which the order of composition does not matter. Show that \(f \circ g=g \circ f\).

Suppose that \(f(x)=x^{4}, x \geq 0\). Find \(g(x)\) so that \(f \circ g=g \circ f\).

Sketch the graph of each function. Do not use a graphing calculator. (Assume the largest possible domain.) $$ y=0.2 \cos (-x) $$

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

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

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

Use a graphing calculator to graph \(f(x)=x^{2}, x \geq 0\), and \(g(x)=x^{4}, x \geq 0\), together. For which values of \(x\) is \(f(x)>g(x)\) and for which is \(f(x)

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 \((0,-1)\)