91Ó°ÊÓ

What is a circle? Without using variables, describe how the definition of a circle can be used to obtain a form of its equation.

Give an example of a circle's equation in standard form. Describe how to find the center and radius for this circle.

Begin by graphing the square root function, \(f(x)=\sqrt{x},\) Then use transformations of this graph to graph the given function. $$g(x)=2 \sqrt{x+2}-2$$

Find and simplify the difference quotient $$\frac{f(x+h)-f(x)}{h}, h \neq 0$$for the given function. $$f(x)=2 x^{2}+x-1$$

Does \((x-3)^{2}+(y-5)^{2}=0\) represent the equation of a circle? If not, describe the graph of this equation.

Does \((x-3)^{2}+(y-5)^{2}=-25\) represent the equation of a circle? What sort of set is the graph of this equation?

Begin by graphing the absolute value function, \(f(x)=|x| .\) Then use transformations of this graph to graph the given function. $$g(x)=|x|+4$$

Find and simplify the difference quotient $$\frac{f(x+h)-f(x)}{h}, h \neq 0$$for the given function. $$f(x)=-2 x^{2}+5 x+7$$

Find and simplify the difference quotient $$\frac{f(x+h)-f(x)}{h}, h \neq 0$$for the given function. $$f(x)=\frac{1}{x}$$

What is the slope of a line and how is it found?