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.

$$f(x)=0.75 x^2+|x|+1$$

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.)

$$f(x)=\sqrt{x-1}+2$$

(a) f(x)=0

(b) $f(x) \geq 0$

(c) $f(x) \leq 0$

If f(x) defines a constant function over $(-\infty, \infty)$, how many elements are in the range of $(f \circ f)(x)$?

In Exercise given below, an equation of the form |f(x)|=|g(x)| is given.

(a) Solve the equation analytically and support the solution graphically.

(b) Solve |f(x)|>|g(x)| graphically.

(c) Solve |f(x)|<|g(x)| graphically.

$$|3 x+1|=|2 x-7|$$

Solve each equation or inequality analytically.

$$|5 x-12|>0$$

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.

$$f(x)=0.5 x^4-2 x^2+1$$

Suppose that the graph of $y=x^2$ is translated in such a way that its domain is $(-\infty, \infty)$ and its range is $[38, \infty)$. What values of h and k can be used if the new function is of the form $y=(x-h)^2+k$?

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

$$f(x)=5, \quad g(x)=x$$

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.

f(x-3)+1

Explain how to solve an equation of the form |ax+b|=|cx+d| analytically.

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

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

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.

$$f(x)=x^5-2 x^3$$

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.)

$$f(x)=\left(x-\frac{1}{2}\right)^2-\frac{81}{4}$$

(a) f(x)=0

(b) $f(x) \geq 0$

(c) $f(x) \leq 0$