91Ó°ÊÓ

Find two numbers adding to 20 such that the sum of their squares is as small as possible.

Find the linear functions satisfying the given conditions. $$f(3)=2 \text { and } f(-3)=-4$$

Let \(f(x)=x^{2}\) and \(g(x)=x^{3}\) (a) Either by hand or with a graphing utility, on the same set of axes draw the graphs of \(f\) and \(g\) on the interval [0,1] (b) Compute and compare the average rates of change of fand \(g\) on the interval [0,1] and on the interval \([0,1 / 2]\)

Find all real numbers (if any) that are fixed points for the given functions. $$G(x)=\frac{1}{2}+x$$

Find the linear functions satisfying the given conditions. $$g(0)=0 \text { and } g(1)=\sqrt{2}$$

The difference of two numbers is \(1 .\) What is the smallest possible value for the sum of their squares?

(a) Find the domain, \(x\) - and \(y\) -intercepts, vertical asymptotes, and horizontal asymptotes for each rational function. (b) Use a graphing utility to graph the function. Check to see that the graph is consistent with your results in part (a). $$y=\left(6 x^{2}-5 x+1\right) /\left(2 x^{2}\right)$$

For each quadratic function, state whether it would make sense to look for a highest or a lowest point on the graph. Then determine the coordinates of that point. (a) \(y=2 x^{2}-8 x+1\) (b) \(y=-3 x^{2}-4 x-9\) (c) \(h=-16 t^{2}+256 t\) (d) \(f(x)=1-(x+1)^{2}\) (e) \(g(t)=t^{2}+1\) (f) \(f(x)=1000 x^{2}-x+100\)

(a) Find the domain, \(x\) - and \(y\) -intercepts, vertical asymptotes, and horizontal asymptotes for each rational function. (b) Use a graphing utility to graph the function. Check to see that the graph is consistent with your results in part (a). $$y=x /\left(x^{2}+x+1\right)$$

Find all real numbers (if any) that are fixed points for the given functions. $$F(x)=(7-2 x) / 8$$