Chapter 4

Solve the equation. Check your answers. $$ \sqrt{3 x+7}=3 x+5 $$

Let a be a positive constant. Match \(f(x)\) with its graph \((a-d)\) without using a calculator. $$ f(x)=\frac{x-a}{x+2} $$

Use division to express the (Dividend) as (Divisor)(Quotient) \(+\) (Remainder) $$\frac{1-x^{2}+x^{3}}{x-1}$$

Solve the polynomial equation. $$ x^{4}-2 x^{3}+x^{2}-2 x=0 $$

Solve the equation. Check your answers. $$ \sqrt{1-x}=x+5 $$

Let a be a positive constant. Match \(f(x)\) with its graph \((a-d)\) without using a calculator. $$ f(x)=\frac{-2 x}{x^{2}-a} $$

Use division to express the (Dividend) as (Divisor)(Quotient) \(+\) (Remainder) $$\frac{x^{3}-x^{2}+x+1}{x^{2}+1}$$

Solve the polynomial equation. $$ x^{4}=x^{3}-4 x^{2} $$

Solve the equation. Check your answers. $$ \sqrt{5 x-6}=x $$

Write a formula \(f(x)\) for a national function so that its graph has the specified asymptotes. Vertical: \(x=-3 ;\) horizontal: \(y=1\)

Use division to express the (Dividend) as (Divisor)(Quotient) \(+\) (Remainder) $$ \frac{2 x^{3}+x^{2}-x+4}{x^{2}+x} $$

Solve the polynomial equation. $$ x^{5}+9 x^{3}=x^{4}+9 x^{2} $$

Solve the equation. Check your answers. $$ x-5=\sqrt{5 x-1} $$

Write a formula \(f(x)\) for a national function so that its graph has the specified asymptotes. Vertical: \(x=4 ;\) horizontal: \(y=-3\)

Use synthetic division to divide the first polymomial by the second. $$x^{3}+2 x^{2}-17 x-10 \quad x+5$$

Solve the polynomial equation. $$ x^{4}+x^{3}=16-8 x-6 x^{2} $$

Solve the equation. Check your answers. $$ \sqrt{x+5}+1=x $$

Write a formula \(f(x)\) for a national function so that its graph has the specified asymptotes. Vertical: \(x=\pm 3 ;\) horizontal: \(y=0\)

Use synthetic division to divide the first polymomial by the second. $$x^{3}-2 x+1 \quad x+4$$

Solve the polynomial equation. $$ x^{4}+2 x^{2}=x^{3} $$

Solve the equation. Check your answers. $$ \sqrt{4-3 x}=x+8 $$

Write a formula \(f(x)\) for a national function so that its graph has the specified asymptotes. Vertical: \(x=-2\) and \(x=4 ;\) horizontal: \(y=5\)

Use synthetic division to divide the first polymomial by the second. $$3 x^{3}-11 x^{2}-20 x+3 \quad\quad\quad x-5$$

Solve the polynomial equation. $$ 3 x^{3}+4 x^{2}+6=x $$

Solve the equation. Check your answers. $$ \sqrt{x+1}+3=\sqrt{3 x+4} $$

Solve the polynomial inequality (a) symbolically and (b) graphically. $$ x^{3}-x>0 $$

Graph \(f\) and identify any asymptotes. $$ f(x)=\frac{1}{x^{2}} $$

Use synthetic division to divide the first polymomial by the second. $$x^{4}-3 x^{3}-5 x^{2}+2 x-16 \quad x-3$$

Solve the polynomial equation. $$ 2 x^{3}+5 x^{2}+x+12=0 $$

Solve the equation. Check your answers. $$ \sqrt{x}=\sqrt{x-5}+1 $$

Solve the polynomial inequality (a) symbolically and (b) graphically. $$ 8 x^{3}<27 $$

Graph \(f\) and identify any asymptotes. $$ f(x)=-\frac{1}{x} $$

Use synthetic division to divide the first polymomial by the second. $$x^{4}-3 x^{3}-4 x^{2}+12 x \quad\quad\quad x-2$$

Electricity \(\quad\) Complex numbers are used in the study of electrical circuits. Impedance \(Z\) (or the opposition to the flow of electricity. voltage \(V\) and current \(I\) can all be represented by complex numbers. They are related by the equation \(Z=\frac{V}{I} .\) Find the value of the missing variable. $$ V=50+98 i \quad I=8+5 i $$

Solve the equation. Check your answers. $$ \sqrt{2 x}-\sqrt{x+1}=1 $$

Solve the polynomial inequality (a) symbolically and (b) graphically. $$ x^{3}+x^{2} \geq 2 x $$

Graph \(f\) and identify any asymptotes. $$ f(x)=\frac{2}{x^{2}} $$

Graph \(f\) and identify any asymptotes. $$ f(x)=-\frac{1}{2 x} $$

Use synthetic division to divide the first polymomial by the second. $$=x^{5}+\frac{1}{4} x^{4}-x^{3}-\frac{1}{4} x^{2}+3 x-\frac{5}{4} \quad x+\frac{1}{4}$$

Electricity \(\quad\) Complex numbers are used in the study of electrical circuits. Impedance \(Z\) (or the opposition to the flow of electricity. voltage \(V\) and current \(I\) can all be represented by complex numbers. They are related by the equation \(Z=\frac{V}{I} .\) Find the value of the missing variable. $$ V=30+60 i \quad I=8+6 i $$

Solve the equation. Check your answers. $$ \sqrt{2 x-4}+2=\sqrt{3 x+4} $$

Solve the polynomial inequality (a) symbolically and (b) graphically. $$ 2 x^{3} \leq 3 x^{2}+5 x $$

Use synthetic division to divide the first polymomial by the second. $$2 x^{5}-x^{4}-x^{3}+4 x+3 \quad\quad\quad x+\frac{1}{2}$$

Electricity \(\quad\) Complex numbers are used in the study of electrical circuits. Impedance \(Z\) (or the opposition to the flow of electricity. voltage \(V\) and current \(I\) can all be represented by complex numbers. They are related by the equation \(Z=\frac{V}{I} .\) Find the value of the missing variable. $$ I=1+2 i \quad Z=3-4 i $$

Solve the equation. Check your answers. $$ \sqrt[3]{z+1}=-3 $$

Solve the polynomial inequality (a) symbolically and (b) graphically. $$ x^{4}-13 x^{2}+36<0 $$

Use transformations of the graph of either \(f(x)=\frac{1}{x}\) or \(h(x)=\frac{1}{x^{2}}\) to sketch a graph of \(y=g(x)\) by hand. Show all asymptotes. Write \(g(x)\) in terms of either \(f(x)\) or \(h(x)\) $$ g(x)=\frac{1}{x-3} $$

Use synthetic division to divide the first polymomial by the second. $$x^{4}-\frac{1}{2} x^{3}+3 x^{2}-\frac{5}{2} x+\frac{9}{2} \quad x-\frac{1}{2}$$

Electricity \(\quad\) Complex numbers are used in the study of electrical circuits. Impedance \(Z\) (or the opposition to the flow of electricity. voltage \(V\) and current \(I\) can all be represented by complex numbers. They are related by the equation \(Z=\frac{V}{I} .\) Find the value of the missing variable. $$ I=\frac{1}{2}+\frac{1}{4} i \quad Z=8-9 i $$

Solve the equation. Check your answers. $$ \sqrt[3]{z}+5=4 $$