Chapter 1

Is the number rational or irrational? $$1.25$$

Set \(f(x)=2 x^{2}-3 x+1\) and \(g(x)=x^{2}+1 / x\) Calculate the indicated value. $$(f+g)(2)$$

Calculate (a) \(f(0),\) (b) \(f(1),(\text { c) } f(-2), \text { (d) } f(3 / 2)\). $$f(x)=2 x^{2}-3 x+2$$

Is the number rational or irrational? \(\frac{17}{7}\).

Solve the inequality and mark the solution set on a number line. $$2+3 x<5$$.

Is the number rational or irrational? $$\sqrt{16 / 9}$$

Calculate (a) \(f(0),\) (b) \(f(1),(\text { c) } f(-2), \text { (d) } f(3 / 2)\). $$f(x)=\frac{2 x-1}{x^{2}+4}$$

Is the number rational or irrational? -6.

Solve the inequality and mark the solution set on a number line. $$\frac{1}{2}(2 x+3)<6$$.

Is the number rational or irrational? $$\sqrt{5}+1$$

Set \(f(x)=2 x^{2}-3 x+1\) and \(g(x)=x^{2}+1 / x\) Calculate the indicated value. $$(f \cdot g)(-2)$$

Is the number rational or irrational? \(2.131313 \ldots=2 . \overline{13}\).

Solve the inequality and mark the solution set on a number line. $$16 x+64 \leq 16$$.

Is the number rational or irrational? $$1.001001001 \ldots$$

Set \(f(x)=2 x^{2}-3 x+1\) and \(g(x)=x^{2}+1 / x\) Calculate the indicated value. $$\left(\frac{f}{g}\right)(1)$$

State whether the function is a polynomial. a rational function (but not a polynomial), or neither a polynomial nor a rational function. If the function is a polynomial, give the degree. $$h(x)=\frac{x^{2}-4}{\sqrt{2}}$$.

Is the number rational or irrational? \(\sqrt{2}-3\).

Solve the inequality and mark the solution set on a number line. $$3 x+5>\frac{1}{4}(x-2)$$.

Find the distance between the points. $$P_{0}(2,7), \quad P_{1}(-4,7)$$

Calculate (a) \(f(0),\) (b) \(f(1),(\text { c) } f(-2), \text { (d) } f(3 / 2)\). $$f(x)=\frac{2 x}{|x+2|+x^{2}}$$

State whether the function is a polynomial. a rational function (but not a polynomial), or neither a polynomial nor a rational function. If the function is a polynomial, give the degree. $$F(x)=\frac{x^{3}-3 x^{3 / 2}+2 x}{x^{2}-1}$$.

Is the number rational or irrational? 0.

Find the midpoint of the line segment \(\overline{P_{0} P_{1}}\). $$P_{0}(2,4) . \quad P_{1}(6,8)$$

Solve the inequality and mark the solution set on a number line. $$\frac{1}{2}(1+x) < \frac{1}{3}(1-x)$$.

State whether the set is bounded above, bounded b.tow, bounded. If the set is bounded above, give an upper bound; if it is bounded below, give a lower bound; if it is bounded, give an upper bound and a lower bound. $$S=\\{x: x \leq 1\\}$$

Set \(f(x)=2 x^{2}-3 x+1\) and \(g(x)=x^{2}+1 / x\) Calculate the indicated value. $$\left(\frac{f+2 g}{f}\right)(-1)$$

Calculate (a) \(f(0),\) (b) \(f(1),(\text { c) } f(-2), \text { (d) } f(3 / 2)\). $$f(x)=1-\frac{1}{(x+1)^{2}}$$

State whether the function is a polynomial. a rational function (but not a polynomial), or neither a polynomial nor a rational function. If the function is a polynomial, give the degree. $$f(x)=5 x^{4}-\pi x^{2}+\frac{1}{2}$$.

Is the number rational or irrational? \(\pi-2\).

Find the midpoint of the line segment \(\overline{P_{0} P_{1}}\). $$P_{0}(3,-1), \quad P_{1}(-1,5)$$

State whether the set is bounded above, bounded b.tow, bounded. If the set is bounded above, give an upper bound; if it is bounded below, give a lower bound; if it is bounded, give an upper bound and a lower bound. $$S=\\{x:|x+2|<3\\}$$

Set \(f(x)=2 x^{2}-3 x+1\) and \(g(x)=x^{2}+1 / x\) Calculate the indicated value. $$(f \circ g)(1)$$

Calculate (a) \(f(-x),\) (b) \(f(1 / x),(c) f(a+b)\). $$f(x)=x^{2}-2 x$$

State whether the function is a polynomial. a rational function (but not a polynomial), or neither a polynomial nor a rational function. If the function is a polynomial, give the degree. $$f(x)=\sqrt{x}(\sqrt{x}+1)$$.

Is the number rational or irrational? \(\sqrt[3]{8}\).

Find the midpoint of the line segment \(\overline{P_{0} P_{1}}\). $$P_{0}(2,-3) . \quad P_{1}(7, \quad 3)$$

Solve the inequality and mark the solution set on a number line. $$x^{2}-1 < 0$$.

Set \(f(x)=2 x^{2}-3 x+1\) and \(g(x)=x^{2}+1 / x\) Calculate the indicated value. $$(g \circ f)(1)$$

Calculate (a) \(f(-x),\) (b) \(f(1 / x),(c) f(a+b)\). $$f(x)=\frac{x}{x^{2}+1}$$

State whether the function is a polynomial. a rational function (but not a polynomial), or neither a polynomial nor a rational function. If the function is a polynomial, give the degree. $$g(x)=\frac{x^{2}-2 x-8}{x+2}$$.

Is the number rational or irrational? 0.125.

Find the midpoint of the line segment \(\overline{P_{0} P_{1}}\). $$P_{0}(a, 3) . \quad P_{1}(3, a)$$

Solve the inequality and mark the solution set on a number line. $$x^{2}+9 x+20 < 0$$.

Find the real roots of the equation. $$2 x^{2}+x-1=0$$

Determine \(f+g, f-g , f \cdot g , f / g,\) and give the domain of each. $$f(x)=2 x-3, g(x)=2-x$$

Calculate (a) \(f(-x),\) (b) \(f(1 / x),(c) f(a+b)\). $$f(x)=\sqrt{1+x^{2}}$$

State whether the function is a polynomial. a rational function (but not a polynomial), or neither a polynomial nor a rational function. If the function is a polynomial, give the degree. $$f(x)=\frac{\sqrt{x^{2}+1}}{x^{2}-1}$$.

Is the number rational or irrational? \(-\sqrt{9}\).

Solve the inequality and mark the solution set on a number line. $$x^{2}-x-6 \geq 0$$.

Find the real roots of the equation. $$x^{2}+2 x+5=0$$