Chapter 3

Find the domain of each rational function. \(f(x)=\frac{5 x}{x-4}\)

Use the four-step procedure for solving variation problems given on page 445 to solve Exercises 1–10. \(y\) varies directly as \(x . y=65\) when \(x=5 .\) Find \(y\) when \(x=12\)

Divide using long division. State the quotient, \(q(x),\) and the remainder, \(r(x)\). $$ \left(x^{2}+8 x+15\right) \div(x+5) $$

Solve each polynomial inequality in Exercises \(1-42\) and graph the solution set on a real number line. Express each solution set in interval notation. $$ (x-4)(x+2)>0 $$

In Exercises 1–8, use the Rational Zero Theorem to list all possible rational zeros for each given function. $$f(x)=x^{3}+x^{2}-4 x-4$$

Determine which functions are polynomial functions. For those that are, identify the degree. \(f(x)=5 x^{2}+6 x^{3}\)

Find the domain of each rational function. $$ f(x)=\frac{7 x}{x-8} $$

Use the four-step procedure for solving variation problems given on page 445 to solve Exercises 1–10. \(y\) varies directly as \(x . y=45\) when \(x=5 .\) Find \(y\) when \(x=13\)

In Exercises 1–10, determine which functions are polynomial functions. For those that are, identify the degree. $$f(x)=7 x^{2}+9 x^{4}$$

Solve each polynomial inequality in Exercises \(1-42\) and graph the solution set on a real number line. Express each solution set in interval notation. $$ (x+3)(x-5)>0 $$

In Exercises 1–8, use the Rational Zero Theorem to list all possible rational zeros for each given function. $$ f(x)=x^{3}+3 x^{2}-6 x-8 $$

Determine which functions are polynomial functions. For those that are, identify the degree. \(f(x)=7 x^{2}+9 x^{4}\)

Find the domain of each rational function. $$ g(x)=\frac{3 x^{2}}{(x-5)(x+4)} $$

To complete the square of \(x^{2}-5 x\), you add the number \(\underline{\quad}.\)

Solve each polynomial inequality in Exercises \(1-42\) and graph the solution set on a real number line. Express each solution set in interval notation. $$ (x-7)(x+3) \leq 0 $$

In Exercises 1–8, use the Rational Zero Theorem to list all possible rational zeros for each given function. $$ f(x)=3 x^{4}-11 x^{3}-x^{2}+19 x+6 $$

Determine which functions are polynomial functions. For those that are, identify the degree. \(g(x)=7 x^{5}-\pi x^{3}+\frac{1}{5} x\)

Find the domain of each rational function. $$ g(x)=\frac{2 x^{2}}{(x-2)(x+6)} $$

In Exercises 1-16, divide using long division. State the quotient, \(q(x),\) and the remainder, \(r(x)\) \(\left(x^{3}-2 x^{2}-5 x+6\right) \div(x-3)\)

Solve each polynomial inequality in Exercises \(1-42\) and graph the solution set on a real number line. Express each solution set in interval notation. $$ (x+1)(x-7) \leq 0 $$

In Exercises 1–8, use the Rational Zero Theorem to list all possible rational zeros for each given function. $$ f(x)=2 x^{4}+3 x^{3}-11 x^{2}-9 x+15 $$

Determine which functions are polynomial functions. For those that are, identify the degree. \(g(x)=6 x^{7}+\pi x^{5}+\frac{2}{3} x\)

Find the domain of each rational function. $$ h(x)=\frac{x+7}{x^{2}-49} $$

Use the four-step procedure for solving variation problems given on page 445 to solve Exercises 1–10. \(y\) varies directly as \(x\) and inversely as the square of \(z . y=20\) when \(x=50\) and \(z=5 .\) Find \(y\) when \(x=3\) and \(z=6\)

In Exercises 1–8, use the Rational Zero Theorem to list all possible rational zeros for each given function. $$ f(x)=4 x^{4}-x^{3}+5 x^{2}-2 x-6 $$

Solve each polynomial inequality in Exercises \(1-42\) and graph the solution set on a real number line. Express each solution set in interval notation. $$ x^{2}-5 x+4>0 $$

Find the domain of each rational function. $$ h(x)=\frac{x+8}{x^{2}-64} $$

Use the four-step procedure for solving variation problems given on page 445 to solve Exercises 1–10. a varies directly as \(b\) and inversely as the square of \(c . a=7\) when \(b=9\) and \(c=6 .\) Find \(a\) when \(b=4\) and \(c=8\)

Solve each polynomial inequality in Exercises \(1-42\) and graph the solution set on a real number line. Express each solution set in interval notation. $$ x^{2}-4 x+3<0 $$

In Exercises 1–8, use the Rational Zero Theorem to list all possible rational zeros for each given function. $$ f(x)=3 x^{4}-11 x^{3}-3 x^{2}-6 x+8 $$

Find the domain of each rational function. $$ f(x)=\frac{x+7}{x^{2}+49} $$

Solve each polynomial inequality in Exercises \(1-42\) and graph the solution set on a real number line. Express each solution set in interval notation. $$ x^{2}+5 x+4>0 $$

Use the four-step procedure for solving variation problems given on page 445 to solve Exercises 1–10. \(y\) varies jointly as \(x\) and \(z . y=25\) when \(x=2\) and \(z=5\) Find \(y\) when \(x=8\) and \(z=12\)

In Exercises 1–8, use the Rational Zero Theorem to list all possible rational zeros for each given function. $$ f(x)=x^{5}-x^{4}-7 x^{3}+7 x^{2}-12 x-12 $$

In Exercises 1–10, determine which functions are polynomial functions. For those that are, identify the degree. $$f(x)=x^{\frac{1}{2}}-3 x^{2}+5$$

Find the domain of each rational function. $$ f(x)=\frac{x+8}{x^{2}+64} $$

Solve each polynomial inequality in Exercises \(1-42\) and graph the solution set on a real number line. Express each solution set in interval notation. $$ x^{2}+x-6>0 $$

Use the four-step procedure for solving variation problems given on page 445 to solve Exercises 1–10. C varies jointly as \(A\) and \(T . C=175\) when \(A=2100\) and \(T=4 .\) Find \(C\) when \(A=2400\) and \(T=6\)

In Exercises 1–10, determine which functions are polynomial functions. For those that are, identify the degree. $$f(x)=x^{\frac{1}{3}}-4 x^{2}+7$$

In Exercises 1–8, use the Rational Zero Theorem to list all possible rational zeros for each given function. $$ f(x)=4 x^{5}-8 x^{4}-x+2 $$

Solve each polynomial inequality in Exercises \(1-42\) and graph the solution set on a real number line. Express each solution set in interval notation. $$ x^{2}-6 x+9<0 $$

In Exercises 1–10, determine which functions are polynomial functions. For those that are, identify the degree. $$f(x)=\frac{x^{2}+7}{x^{3}}$$

In Exercises 9–16, a. List all possible rational zeros b. Use syntheric division to test the possible rational zeros and find an actual zera c. Use the quotient from part (b) to find the remaining zeros of the polynomial function. $$ f(x)=x^{3}+x^{2}-4 x-4 $$

Find the coordinates of the vertex for the parabola defined by the given quadratic function. $$ f(x)=2(x-3)^{2}+1 $$

Solve each polynomial inequality in Exercises \(1-42\) and graph the solution set on a real number line. Express each solution set in interval notation. $$ x^{2}-2 x+1>0 $$

Determine which functions are polynomial functions. For those that are, identify the degree. \(f(x)=\frac{x^{2}+7}{3}\)

In Exercises 1–10, determine which functions are polynomial functions. For those that are, identify the degree. $$f(x)=\frac{x^{2}+7}{3}$$

In Exercises 9–16, a. List all possible rational zeros b. Use syntheric division to test the possible rational zeros and find an actual zera c. Use the quotient from part (b) to find the remaining zeros of the polynomial function. $$ f(x)=x^{3}-2 x^{2}-11 x+12 $$

Find the coordinates of the vertex for the parabola defined by the given quadratic function. $$ f(x)=-3(x-2)^{2}+12 $$

Solve each polynomial inequality in Exercises \(1-42\) and graph the solution set on a real number line. Express each solution set in interval notation. $$ 3 x^{2}+10 x-8 \leq 0 $$