91Ó°ÊÓ

Suppose the graph of a function \(f\) is known. Then the graph of \(y=f(x-2)\) is obtained by a __________ shift of the graph of \(f\) to the ___________ a distance of 2 units.

The intercepts of the equation \(x^{2}+4 y^{2}=16\) are ______.

The interval (2,5) can be written as the inequality _________________

Let \(P=(x, y)\) be a point on the graph of \(y=x^{2}-8\) (a) Express the distance \(d\) from \(P\) to the origin as a function of \(x\). (b) What is \(d\) if \(x=0 ?\) (c) What is \(d\) if \(x=1 ?\) (d) Use a graphing utility to graph \(d=d(x)\). (e) For what values of \(x\) is \(d\) smallest?

Graph \(y=\frac{1}{x}\)

Let \(P=(x, y)\) be a point on the graph of \(y=x^{2}-8\) (a) Express the distance \(d\) from \(P\) to the point (0,-1) as a function of \(x\). (b) What is \(d\) if \(x=0 ?\) (c) What is \(d\) if \(x=-1 ?\) (d) Use a graphing utility to graph \(d=d(x)\). (e) For what values of \(x\) is \(d\) smallest?

True or False. The point (-2,-6) is on the graph of the equation \(x=2 y-2\).

If \(x=-2,\) the value of the expression \(3 x^{2}-5 x+\frac{1}{x}\) is ___________

Suppose the graph of a function \(f\) is known. Then the graph of \(y=f(-x)\) is a reflection about the __________ -axis of the graph of the function \(y=f(x)\).

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?