91Ó°ÊÓ

A quadratic function is given. (a) Express the quadratic function in standard form. (b) Find its vertex and its \(x\) - and \(y\) -intercept(s). (c) Sketch its graph. $$f(x)=x^{2}+8 x$$

Express the function (or rule) in words. $$g(x)=\frac{x}{3}-4$$

Find \(f+g, f-g, f g,\) and \(f / g\) and their domains. $$f(x)=\frac{2}{x+1}, \quad g(x)=\frac{x}{x+1}$$

A function \(f\) is given. (a) Use a graphing device to draw the graph of \(f\) (b) State approximately the intervals on which \(f\) is increasing and on which \(f\) is decreasing. $$f(x)=4-x^{2 / 3}$$

In these exercises you are asked to find a function that models a real-life situation. Use the guidelines for modeling described in the text to help you. Area A rectangle has a perimeter of \(20 \mathrm{ft}\). Find a function that models its area \(A\) in terms of the length \(x\) of one of its sides.

Suppose the graph of \(f\) is given. Describe how the graph of each function can be obtained from the graph of \(f .\) (a) \(y=-f(x)+5\) (b) \(y=3 f(x)-5\)

Sketch the graph of the function by first making a table of values. $$f(x)=\frac{x-3}{2}, \quad 0 \leq x \leq 5$$

In these exercises you are asked to find a function that models a real-life situation. Use the guidelines for modeling described in the text to help you. Area Find a function that models the area \(A\) of an equilateral triangle in terms of the length \(x\) of one of its sides.

A quadratic function is given. (a) Express the quadratic function in standard form. (b) Find its vertex and its \(x\) - and \(y\) -intercept(s). (c) Sketch its graph. $$f(x)=2 x^{2}+6 x$$

Suppose the graph of \(f\) is given. Describe how the graph of each function can be obtained from the graph of \(f .\) (a) \(y=f(x-4)+\frac{3}{4}\) (b) \(y=f(x+4)-\frac{3}{4}\)