91Ó°ÊÓ

Exercises \(51-60\) tell by what factor and direction the graphs of the given functions are to be stretched or compressed. Give an equation for the stretched or compressed graph . $$ y=\sqrt{x+1}, \quad \text { stretched vertically by a factor of } 3 $$

Exercises \(51-60\) tell by what factor and direction the graphs of the given functions are to be stretched or compressed. Give an equation for the stretched or compressed graph . $$ y=\sqrt{4-x^{2}}, \quad \text { stretched horizontally by a factor of } 2 $$

Graph the parabolas in Exercises 53–60. Label the vertex, axis, and intercepts in each case. $$ y=-x^{2}-6 x-5 $$

Exercises \(51-60\) tell by what factor and direction the graphs of the given functions are to be stretched or compressed. Give an equation for the stretched or compressed graph. \(y=\sqrt{4-x^{2}}, \quad\) compressed vertically by a factor of 3

Graph the parabolas in Exercises 53–60. Label the vertex, axis, and intercepts in each case. $$ y=2 x^{2}-x+3 $$

A triangle has sides \(a=2\) and \(b=3\) and angle \(C=60^{\circ}\) (as in Exercise \(55 ) .\) Find the sine of angle \(B\) using the law of sines.

A triangle has side \(c=2\) and angles \(A=\pi / 4\) and \(B=\pi / 3\) . Find the length \(a\) of the side opposite \(A .\)

Graph the parabolas in Exercises 53–60. Label the vertex, axis, and intercepts in each case. $$ y=\frac{1}{2} x^{2}+x+4 $$

Exercises \(51-60\) tell by what factor and direction the graphs of the given functions are to be stretched or compressed. Give an equation for the stretched or compressed graph . $$ y=\sqrt{4-x^{2}}, \quad \text { compressed vertically by a factor of } 3 $$

Exercises \(51-60\) tell by what factor and direction the graphs of the given functions are to be stretched or compressed. Give an equation for the stretched or compressed graph . $$ y=1-x^{3}, \quad \text { stretched horizontally by a factor of } 2 $$