Solve each equation or inequality analytically.

$$|2 x+5| \geq 7$$

Let the domain of f(x) be [-1,2]$ and the range be [0,3]. Find the domain and range of each of the following.

-f(x)

In Exercise given below, use f(x) and g(x) to find each composition. Identify its domain. Do not use a calculator. (a) $(f \circ g)(x) \quad$ (b) $(g \circ f)(x) \quad$ (c) $(f \circ f)(x)$

$$f(x)=2 x+1, \quad g(x)=4 x^3-5 x^2$$

Use the analytic method of Example mentioned to determine whether the graph of the given function is symmetric with respect to the y-axis, symmetric with respect to the origin, or neither. Use your calculator and the standard window to support your conclusion.

$$f(x)=-x^3+2 x$$

Let the domain of f(x) be [-1,2]$ and the range be [0,3]. Find the domain and range of each of the following.

5f(x+1)

Solve each equation or inequality analytically.

$$|2 x+5| \leq 7$$

Use the x-intercept method and the given graph to solve each equation or inequality. (Hint: Extend the concepts of Section mentioned for graphical solution of linear equations and inequalities.)

$$f(x)=(x-\sqrt{2})^3$$

(a) f(x)=0

(b) f(x)>0

(c) f(x)<0

The table lists the average annual costs (in dollars) of tuition and fees at public four-year colleges for selected years.

Source: The College Board.

(a) Use a calculator to find the least-squares regression line for these data, where x=0 corresponds to 1993, x=2 corresponds to 1995 , and so on.

(b) Based on your result from part (a), write an equation that yields the same y-values when the exact year is entered.

(c) Estimate the cost of tuition and fees in 2009 to the nearest hundred dollars.

Solve each equation or inequality.

$$|7 x-5| \geq-5$$

The graph is a translation of y=|x|. What are the values of h and k if the equation is of the form y=|x-h|+k?

Solve each equation or inequality.

$$\left|\frac{3}{4} x-\frac{1}{2}\right|<-4$$

In Exercise given below, each function is either even or odd. Determine f(-x) and state which situation applies.

$$f(x)=4 x-\frac{1}{x}$$

The linear equation

$$y=726.7 x+7421.6$$

gives an approximation of the total public debt y (in billions of dollars), where x=0 corresponds to 2005 , x=1 corresponds to 2006, and so on. (Source: www. treasurydirect.gov)

(a) Write an equation that yields the same y-values when the exact year is entered.

(b) Predict the total public debt in 2012.

In Exercise given below, use f(x) and g(x) to find each composition. Identify its domain. Do not use a calculator. (a) $(f \circ g)(x) \quad$ (b) $(g \circ f)(x) \quad$ (c) $(f \circ f)(x)$

$$f(x)=x+4, \quad g(x)=\sqrt{4-x^2}$$