91Ó°ÊÓ

Find the intercepts of the equation \(y=x^{3}-8\)

Test the equation \(y=5 x^{2}-1\) for symmetry with respect to the \(x\) -axis, the \(y\) -axis, and the origin.

Let \(P=(x, y)\) be a point on the graph of \(y=\sqrt{x}\) (a) Express the distance \(d\) from \(P\) to the point (1,0) as a function of \(x\). (b) Use a graphing utility to graph \(d=d(x)\). (c) For what values of \(x\) is \(d\) smallest? (d) What is the smallest distance?

Write the point-slope form of the line with slope 5 containing the point (3,-2)

True or False The graph of \(y=-f(x)\) is the reflection about the \(x\) -axis of the graph of \(y=f(x)\).

Let \(P=(x, y)\) be a point on the graph of \(y=\frac{1}{x}\) (a) Express the distance \(d\) from \(P\) to the origin as a function of \(x\). (b) Use a graphing utility to graph \(d=d(x)\). (c) For what values of \(x\) is \(d\) smallest? (d) What is the smallest distance?

Find \(a\) so that the point (-1,2) is on the graph of \(f(x)=a x^{2}+4\)

Multiple Choice Which function has a graph that is the graph of \(y=\sqrt{x}\) shifted down 3 units? (a) \(y=\sqrt{x+3}\) (b) \(y=\sqrt{x-3}\) (c) \(y=\sqrt{x}+3\) (d) \(y=\sqrt{x}-3\)

True or False The cube function is odd and is increasing on the interval \((-\infty, \infty)\)

A right triangle has one vertex on the graph of \(y=9-x^{2}, x>0,\) at \((x, y),\) another at the origin, and the third on the positive \(x\) -axis at \((x, 0) .\) Express the area \(A\) of the triangle as a function of \(x\).