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) $(f \circ f)(x)$

$$f(x)=\frac{x-3}{2}, g(x)=2 x+3$$

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)

Solve each equation or inequality analytically.

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

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.

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

Solve each equation or inequality.

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

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.

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?

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

Solve each equation or inequality analytically.

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

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.

5f(x+1)

Consider the two functions in the figure.

(a) Find a value of c for which g(x)=f(x)+c.

(b) Find a value of c for which g(x)=f(x+c).

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) $(f \circ f)(x)$

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

Solve each equation or inequality.

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

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.