Chapter 2

These exercises correspond to the Just in Time references in this section. Complete them to review topics relevant to the remaining exercises. Factor: \(x^{2}-13 x+40\)

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

A quotient of two polynomial expressions is called a _____ and is defined whenever the denominator is not equal to ____.

These exercises correspond to the Just in Time references in this section. Complete them to review topics relevant to the remaining exercises. The graph of \(g(x)=f(x)-3\) is the graph of \(f(x)\) shifted _________ 3 units.

True or False: The variable \(x\) in \(f(x)\) is a placeholder and can be replaced by any quantity as long as the same replacement occurs in the expression for the function.

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

Multiply. $$(x-2)\left(\frac{3}{x-2}\right)$$

These exercises correspond to the Just in Time references in this section. Complete them to review topics relevant to the remaining exercises. The graph of \(g(x)=f(x+2)\) is the graph of \(f(x)\) shifted ___________ 2 units.

What is the domain of the function \(f(x)=x^{2}-3 x ?\)

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

Multiply. $$x^{2}\left(\frac{5}{x}\right)$$

These exercises correspond to the Just in Time references in this section. Complete them to review topics relevant to the remaining exercises. Factor: \(4 x^{2}+12 x+9\)

What is the domain of the function \(f(x)=\sqrt{x-1} ?\)

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

Multiply. $$x(x-5)\left(\frac{2}{x}\right)$$

Use the quadratic formula to solve the equation. $$x^{2}-5 x+3=0$$

What is the domain of the function \(f(x)=\sqrt{x^{2}-9} ?\)

Factor: \(x^{2}-16 x+64\)

Find the constant term needed to make \(x^{2}-6 x\) a perfect square trinomial.

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

Multiply. $$(2 x+1)(x-3)\left(\frac{x+7}{x-3}\right)$$

Use the quadratic formula to solve the equation. $$2 x^{2}+x-5=0$$

What is the domain of the function \(f(x)=\frac{x+2}{x-1} ?\)

Factor: \(25 y^{2}+10 y+1\)

Find the constant term needed to make \(x^{2}+7 x\) a perfect square trinomial.

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

Solve the polynomial equation. In Exercises \(7-14,\) find all solutions. In Exercises \(15-18,\) find only real solutions. Check your solutions. $$x^{4}-49=0$$

Use the quadratic formula to solve the equation. $$x^{2}-3 x-2=0$$

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) \(\left(\frac{f}{g}\right)(x)\) $$f(x)=3 x-5 ; g(x)=-x+3$$

Write the expression in the form \((a x+b)^{2}: x^{2}-8 x+16\).

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

Decide if each function is odd, ezen, or neither by using the appropriate definitions. $$\begin{array}{cccccc}x & -4 & -2 & 0 & 2 & 4 \\\\\hline f(x) & 17 & 5 & 1 & 5 & 17\end{array}$$

Solve the polynomial equation. In Exercises \(7-14,\) find all solutions. In Exercises \(15-18,\) find only real solutions. Check your solutions. $$x^{4}-25=0$$

Use the quadratic formula to solve the equation. $$x^{2}+x-4=0$$

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) \(\left(\frac{f}{g}\right)(x)\) $$f(x)=2 x+1 ; g(x)=-5 x-1$$

What number must be added to write the expression in the form \((x+b)^{2} ?\) $$ x^{2}-14 x $$

Write the expression in the form \((a x+b)^{2}: 9 x^{2}-30 x+25\).

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

Decide if each function is odd, ezen, or neither by using the appropriate definitions. $$\begin{array}{|cccccc}x & -3 & -1 & 0 & 1 & 3 \\\\\hline f(x) & 10 & 3 & -2 & 4 & 10\end{array}$$

Solve the polynomial equation. In Exercises \(7-14,\) find all solutions. In Exercises \(15-18,\) find only real solutions. Check your solutions. $$x^{4}-10 x^{2}=-21$$

Write the number as a pure imaginary number. $$\sqrt{-16}$$

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) \(\left(\frac{f}{g}\right)(x)\) $$f(x)=x-3 ; g(x)=x^{2}+1$$

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. $$f(x)=-2 x^{2}, g(x)=-x^{2}$$

Solve the quadratic equation by factoring. $$x^{2}-25=0$$

Identify the underlying basic function, and use transformations of the basic function to sketch the graph of the given function. $$f(x)=\sqrt{x-4}$$

Decide if each function is odd, ezen, or neither by using the appropriate definitions. $$\begin{array}{cccccc}x & -4 & -2 & 0 & 2 & 4 \\\\\hline f(x) & -3 & -1 & 0 & 1 & 3\end{array}$$

Solve the polynomial equation. In Exercises \(7-14,\) find all solutions. In Exercises \(15-18,\) find only real solutions. Check your solutions. $$x^{4}-5 x^{2}=24$$

Write the number as a pure imaginary number. $$\sqrt{-64}$$

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) \(\left(\frac{f}{g}\right)(x)\) $$f(x)=x^{3} ; g(x)=3 x^{2}+4$$

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. $$f(x)=3 x^{2}, g(x)=x^{2}$$