91Ó°ÊÓ

Explain how to use the general form of a line's equation to find the line's slope and \(y\) -intercept.

The regular price of a computer is \(x\) dollars. Let \(f(x)=x-400\) and \(g(x)=0.75 x\) a. Describe what the functions \(f\) and \(g\) model in terms of the price of the computer. b. Find \((f \circ g)(x)\) and describe what this models in terms of the price of the computer. c. Repeat part (b) for \((g \circ f)(x)\) d. Which composite function models the greater discount on the computer, \(f \circ g\) or \(g \circ f ?\) Explain.

If a function is defined by an equation, explain how to find its domain.

Begin by graphing the standard cubic function, \(f(x)=x^{3} .\) Then use transformations of this graph to graph the given function. $$r(x)=(x-2)^{3}+1$$

Explain how to find the difference quotient of a function \(f\) \(\frac{f(x+h)-f(x)}{h},\) if an equation for \(f\) is given.

The function $$ f(x)=-0.00002 x^{3}+0.008 x^{2}-0.3 x+6.95 $$ models the number of annual physician visits, \(f(x),\) by a person of age \(x .\) Graph the function in a \([0,100,5]\) by \([0,40,2]\) viewing rectangle. What does the shape of the graph indicate about the relationship between one's age and the number of annual physician visits? Use the \([\mathrm{TABLE}]\) or minimum function capability to find the coordinates of the minimum point on the graph of the function. What does this mean?

Find the coefficients that must be placed in each shaded area so that the function's graph will be a line satisfying the specified conditions. \(x+\quad y-12=0 ; x\) -intercept \(=-2 ; y\) -intercept \(=4\)

Explain how the vertical line test is used to determine whether a graph represents a function.

Explain how to identify the domain and range of a function from its graph.

Use transformations of the graph of the greatest integer function, \(f(x)=\operatorname{int}(x),\) to graph each function. $$g(x)=2 \operatorname{int}(x+1)$$