Chapter 2

Solve the quadratic equation by factoring. $$x^{2}-16=0$$

Identify the underlying basic function, and use transformations of the basic function to sketch the graph of the given function. $$f(x)=\sqrt{x+3}$$

Decide if each function is odd, ezen, or neither by using the appropriate definitions. $$\begin{array}{cccccc}x & -3 & -1 & 0 & 1 & 3 \\\f(x) & -5 & -7 & -10 & -7 & -5\end{array}$$

Solve the polynomial equation. In Exercises \(7-14,\) find all solutions. In Exercises \(15-18,\) find only real solutions. Check your solutions. $$6 s^{4}-s^{2}-2=0$$

Write the number as a pure imaginary number. $$\sqrt{-12}$$

In Exercises \(7-16,\) for the given functions \(f\) and \(g,\) find each composite function and identify its domain. (a) \((f+g)(x)\) (b) \((f-g)(x)\) (c) \((f g)(x)\) (d) \(\left(\frac{f}{g}\right)(x)\) $$f(x)=\frac{1}{x} ; g(x)=\frac{1}{2 x-1}$$

This set of exercises will reinforce the skills illustrated in this section. Graph each pair of functions on the same set of coordinate axes, and find the domain and range of each function. $$f(x)=\frac{1}{2} x^{2}, g(x)=2 x^{2}$$

Solve the quadratic equation by factoring. $$x^{2}-7 x+12=0$$

Identify the underlying basic function, and use transformations of the basic function to sketch the graph of the given function. $$H(x)=|x-2|+1$$

Solve the polynomial equation. In Exercises \(7-14,\) find all solutions. In Exercises \(15-18,\) find only real solutions. Check your solutions. $$4 s^{4}+11 s^{2}-3=0$$

Write the number as a pure imaginary number. $$\sqrt{-24}$$

In Exercises \(7-16,\) for the given functions \(f\) and \(g,\) find each composite function and identify its domain. (a) \((f+g)(x)\) (b) \((f-g)(x)\) (c) \((f g)(x)\) (d) \(\left(\frac{f}{g}\right)(x)\) $$f(x)=\frac{2}{x+1} ; g(x)=\frac{-1}{x^{2}}$$

This set of exercises will reinforce the skills illustrated in this section. Graph each pair of functions on the same set of coordinate axes, and find the domain and range of each function. $$f(x)=-x^{2}, g(x)=-\frac{1}{2} x^{2}$$

Solve the quadratic equation by factoring. $$x^{2}-4 x-21=0$$

Identify the underlying basic function, and use transformations of the basic function to sketch the graph of the given function. $$G(x)=\sqrt{x+1}-2$$

Solve the polynomial equation. In Exercises \(7-14,\) find all solutions. In Exercises \(15-18,\) find only real solutions. Check your solutions. $$4 x^{4}-7 x^{2}=2$$

Use the following table of test values of the quadratic functions \(f\) and \(g\) defined on \((-\infty, \infty)\). $$\begin{array}{ccc} t & f(t) & g(t) \\ -1 & 0 & 2 \\ -0.5 & 0.5 & 1.25 \\ 0 & 1 & 1 \\ 0.5 & 1.5 & 1.25 \\ 1 & 2 & 2 \\ 1.5 & 2.5 & 3.25 \\ 2 & 3 & 5 \\ 2.5 & 3.5 & 7.25 \\ 3 & 4 & 10 \end{array}$$ Find the region(s) where \(f(t) \geq g(t)\).

Write the number as a pure imaginary number. $$\sqrt{-\frac{4}{25}}$$

In Exercises \(7-16,\) for the given functions \(f\) and \(g,\) find each composite function and identify its domain. (a) \((f+g)(x)\) (b) \((f-g)(x)\) (c) \((f g)(x)\) (d) \(\left(\frac{f}{g}\right)(x)\) $$f(x)=\sqrt{x} ; g(x)=-x+1$$

This set of exercises will reinforce the skills illustrated in this section. Graph each pair of functions on the same set of coordinate axes, and find the domain and range of each function. $$f(x)=x^{2}+1, g(x)=x^{2}-1$$

Solve the quadratic equation by factoring. $$-3 x^{2}+12=0$$

Identify the underlying basic function, and use transformations of the basic function to sketch the graph of the given function. $$S(x)=(x+3)^{2}-1$$

Use the following table of test values of the quadratic functions \(f\) and \(g\) defined on \((-\infty, \infty)\). $$\begin{array}{ccc} t & f(t) & g(t) \\ -1 & 0 & 2 \\ -0.5 & 0.5 & 1.25 \\ 0 & 1 & 1 \\ 0.5 & 1.5 & 1.25 \\ 1 & 2 & 2 \\ 1.5 & 2.5 & 3.25 \\ 2 & 3 & 5 \\ 2.5 & 3.5 & 7.25 \\ 3 & 4 & 10 \end{array}$$ Find the region(s) where \(f(t) \leq g(t)\).

Solve the polynomial equation. In Exercises \(7-14,\) find all solutions. In Exercises \(15-18,\) find only real solutions. Check your solutions. $$-x^{4}+2 x^{2}-1=0$$

Write the number as a pure imaginary number. $$\sqrt{-\frac{9}{4}}$$

In Exercises \(7-16,\) for the given functions \(f\) and \(g,\) find each composite function and identify its domain. (a) \((f+g)(x)\) (b) \((f-g)(x)\) (c) \((f g)(x)\) (d) \(\left(\frac{f}{g}\right)(x)\) $$f(x)=2 x-1 ; g(x)=\sqrt{x}$$

This set of exercises will reinforce the skills illustrated in this section. Graph each pair of functions on the same set of coordinate axes, and find the domain and range of each function. $$f(x)=-x^{2}+2, g(x)=-x^{2}-2$$

Solve the quadratic equation by factoring. $$-5 x^{2}+45=0$$

Identify the underlying basic function, and use transformations of the basic function to sketch the graph of the given function. $$g(x)=(x-2)^{2}+5$$

Solve the inequality by factoring. $$x^{2}-1 \leq 0$$

Solve the polynomial equation. In Exercises \(7-14,\) find all solutions. In Exercises \(15-18,\) find only real solutions. Check your solutions. $$x^{6}-4 x^{3}=5$$

Use the definition of i to solve the equation. $$x^{2}=-16$$

In Exercises \(7-16,\) for the given functions \(f\) and \(g,\) find each composite function and identify its domain. (a) \((f+g)(x)\) (b) \((f-g)(x)\) (c) \((f g)(x)\) (d) \(\left(\frac{f}{g}\right)(x)\) $$f(x)=|x| ; g(x)=\frac{1}{2 x+5}$$

This set of exercises will reinforce the skills illustrated in this section. Graph each pair of functions on the same set of coordinate axes, and find the domain and range of each function. $$f(x)=(x+1)^{2}, \quad g(x)=x^{2}$$

Solve the quadratic equation by factoring. $$6 x^{2}-x-2=0$$

Identify the underlying basic function, and use transformations of the basic function to sketch the graph of the given function. $$H(t)=3 t^{2}$$

Solve the inequality by factoring. $$x^{2}-9<0$$

Solve the polynomial equation. In Exercises \(7-14,\) find all solutions. In Exercises \(15-18,\) find only real solutions. Check your solutions. $$x^{6}=x^{3}+6$$

Use the definition of i to solve the equation. $$x^{2}=-25$$

In Exercises \(7-16,\) for the given functions \(f\) and \(g,\) find each composite function and identify its domain. (a) \((f+g)(x)\) (b) \((f-g)(x)\) (c) \((f g)(x)\) (d) \(\left(\frac{f}{g}\right)(x)\) $$f(x)=\frac{2}{x-4} ; g(x)=-|x|$$

This set of exercises will reinforce the skills illustrated in this section. Graph each pair of functions on the same set of coordinate axes, and find the domain and range of each function. $$f(x)=-(x-3)^{2}, \quad g(x)=-x^{2}$$

Solve the quadratic equation by factoring. $$5 x^{2}-7 x-6=0$$

Identify the underlying basic function, and use transformations of the basic function to sketch the graph of the given function. $$g(x)=2 \sqrt{x}$$

Solve the inequality by factoring. $$2 x^{2}+3 x \geq 5$$

Solve the polynomial equation. In Exercises \(7-14,\) find all solutions. In Exercises \(15-18,\) find only real solutions. Check your solutions. $$3 t^{6}+14 t^{3}=-8$$

In Exercises \(17-40,\) let \(f(x)=-x^{2}+x, g(x)=\frac{2}{x+1},\) and \(h(x)=-2 x+1 .\) Evaluate each of the following. $$(f+g)(1)$$

This set of exercises will reinforce the skills illustrated in this section. Graph each pair of functions on the same set of coordinate axes, and find the domain and range of each function. $$f(x)=(x+2)^{2}, \quad g(x)=(x-2)^{2}$$

Solve the quadratic equation by factoring. $$4 x^{2}-4 x+1=0$$

Identify the underlying basic function, and use transformations of the basic function to sketch the graph of the given function. $$S(x)=-4|x|$$

Solve the inequality by factoring. $$-2 x^{2}-3 x>2$$