Chapter 5

For the following exercises, write an equation describing the relationship of the given variables. \(y\) varies inversely as the square root of \(x\) and when \(x=25, \quad y=3\).

For the following exercises, find the inverse of the functions. $$ f(x)=4-x^{3} $$

For the following exercises, find the domain, vertical asymptotes, and horizontal asymptotes of the functions. $$ f(x)=\frac{3+x}{x^{3}-27} $$

For the following exercises, use the Factor Theorem to find all real zeros for the given polynomial function and one factor. $$ f(x)=2 x^{3}-9 x^{2}+13 x-6 ; \quad x-1 $$

For the following exercises, use synthetic division to find the quotient. Ensure the equation is in the form required by synthetic division. (Hint: divide the dividend and divisor by the coefficient of the linear term in the divisor.) $$ \left(3 x^{3}-2 x^{2}+x-4\right) \div(x+3) $$

For the following exercises, find the \(x\) - or t-intercepts of the polynomial functions. $$ f(x)=x^{3}+6 x^{2}-7 x $$

For the following exercises, find the degree and leading coefficient for the given polynomial. $$ -2 x^{2}-3 x^{5}+x-6 $$

For the following exercises, determine whether there is a minimum or maximum value to each quadratic function. Find the value and the axis of symmetry. $$ y(x)=2 x^{2}+10 x+12 $$

For the following exercises, write an equation describing the relationship of the given variables. \(y\) varies inversely as the cube root of \(x\) and when \(x=64, \quad y=5\).

For the following exercises, find the inverse of the functions. $$ f(x)=4-2 x^{3} $$

For the following exercises, find the domain, vertical asymptotes, and horizontal asymptotes of the functions. $$ f(x)=\frac{3 x-4}{x^{3}-16 x} $$

For the following exercises, use the Factor Theorem to find all real zeros for the given polynomial function and one factor. $$ f(x)=2 x^{3}+x^{2}-5 x+2 ; \quad x+2 $$

For the following exercises, use synthetic division to find the quotient. Ensure the equation is in the form required by synthetic division. (Hint: divide the dividend and divisor by the coefficient of the linear term in the divisor.) $$ \left(2 x^{3}-6 x^{2}-7 x+6\right) \div(x-4) $$

For the following exercises, find the \(x\) - or t-intercepts of the polynomial functions. $$ f(x)=x^{3}+x^{2}-4 x-4 $$

For the following exercises, find the degree and leading coefficient for the given polynomial. $$ x\left(4-x^{2}\right)(2 x+1) $$

For the following exercises, determine whether there is a minimum or maximum value to each quadratic function. Find the value and the axis of symmetry. $$ f(x)=2 x^{2}-10 x+4 $$

For the following exercises, write an equation describing the relationship of the given variables. \(y\) varies jointly with \(x\) and \(z\) and when \(x=2\) and \(z=3, \quad y=36\).

For the following exercises, find the inverse of the functions. $$ f(x)=\sqrt{2 x+1} $$

For the following exercises, find the domain, vertical asymptotes, and horizontal asymptotes of the functions. $$ f(x)=\frac{x^{2}-1}{x^{3}+9 x^{2}+14 x} $$

For the following exercises, use the Factor Theorem to find all real zeros for the given polynomial function and one factor. $$ f(x)=3 x^{3}+x^{2}-20 x+12 ; \quad x+3 $$

For the following exercises, use synthetic division to find the quotient. Ensure the equation is in the form required by synthetic division. (Hint: divide the dividend and divisor by the coefficient of the linear term in the divisor.) $$ \left(6 x^{3}-10 x^{2}-7 x-15\right) \div(x+1) $$

For the following exercises, find the \(x\) - or t-intercepts of the polynomial functions. $$ f(x)=x^{3}+2 x^{2}-9 x-18 $$

For the following exercises, find the degree and leading coefficient for the given polynomial. $$ x^{2}(2 x-3)^{2} $$

For the following exercises, determine whether there is a minimum or maximum value to each quadratic function. Find the value and the axis of symmetry. $$ f(x)=-x^{2}+4 x+3 $$

For the following exercises, write an equation describing the relationship of the given variables. \(y\) varies jointly as \(x, z,\) and \(w\) and when \(x=1, \quad z=2, \quad w=5,\) then \(y=100\).

For the following exercises, find the inverse of the functions. $$ f(x)=\sqrt{3-4 x} $$

For the following exercises, find the domain, vertical asymptotes, and horizontal asymptotes of the functions. $$ f(x)=\frac{x+5}{x^{2}-25} $$

For the following exercises, use the Factor Theorem to find all real zeros for the given polynomial function and one factor. $$ f(x)=2 x^{3}+3 x^{2}+x+6 ; \quad x+2 $$

For the following exercises, use synthetic division to find the quotient. Ensure the equation is in the form required by synthetic division. (Hint: divide the dividend and divisor by the coefficient of the linear term in the divisor.) $$ \left(4 x^{3}-12 x^{2}-5 x-1\right) \div(2 x+1) $$

For the following exercises, find the \(x\) - or t-intercepts of the polynomial functions. $$ f(x)=2 x^{3}-x^{2}-8 x+4 $$

For the following exercises, determine the end behavior of the functions. $$ f(x)=x^{4} $$

For the following exercises, determine whether there is a minimum or maximum value to each quadratic function. Find the value and the axis of symmetry. $$ f(x)=4 x^{2}+x-1 $$

For the following exercises, write an equation describing the relationship of the given variables. \(y\) varies jointly as the square of \(x\) and the square of \(z\) and when \(x=3\) and \(z=4,\) then \(y=72\).

For the following exercises, find the inverse of the functions. $$ f(x)=9+\sqrt{4 x-4} $$

For the following exercises, find the domain, vertical asymptotes, and horizontal asymptotes of the functions. $$ f(x)=\frac{x-4}{x-6} $$

For the following exercises, use the Factor Theorem to find all real zeros for the given polynomial function and one factor. \(f(x)=-5 x^{3}+16 x^{2}-9 ; \quad x-3\)

For the following exercises, use synthetic division to find the quotient. Ensure the equation is in the form required by synthetic division. (Hint: divide the dividend and divisor by the coefficient of the linear term in the divisor.) $$ \left(9 x^{3}-9 x^{2}+18 x+5\right) \div(3 x-1) $$

For the following exercises, find the \(x\) - or t-intercepts of the polynomial functions. $$ f(x)=x^{6}-7 x^{3}-8 $$

For the following exercises, determine the end behavior of the functions. $$ f(x)=x^{3} $$

For the following exercises, determine whether there is a minimum or maximum value to each quadratic function. Find the value and the axis of symmetry. $$ h(t)=-4 t^{2}+6 t-1 $$

For the following exercises, write an equation describing the relationship of the given variables. \(y\) varies jointly as \(x\) and the square root of \(z\) and when \(x=2\) and \(z=25,\) then \(y=100\).

For the following exercises, find the inverse of the functions. $$ f(x)=\sqrt{6 x-8}+5 $$

For the following exercises, find the domain, vertical asymptotes, and horizontal asymptotes of the functions. $$ f(x)=\frac{4-2 x}{3 x-1} $$

For the following exercises, use the Factor Theorem to find all real zeros for the given polynomial function and one factor. $$ x^{3}+3 x^{2}+4 x+12 ; \quad x+3 $$

For the following exercises, use synthetic division to find the quotient. Ensure the equation is in the form required by synthetic division. (Hint: divide the dividend and divisor by the coefficient of the linear term in the divisor.) $$ \left(3 x^{3}-2 x^{2}+x-4\right) \div(x+3) $$

For the following exercises, find the \(x\) - or t-intercepts of the polynomial functions. $$ f(x)=2 x^{4}+6 x^{2}-8 $$

For the following exercises, determine the end behavior of the functions. $$ f(x)=-x^{4} $$

For the following exercises, determine whether there is a minimum or maximum value to each quadratic function. Find the value and the axis of symmetry. $$ f(x)=\frac{1}{2} x^{2}+3 x+1 $$

For the following exercises, write an equation describing the relationship of the given variables. \(y\) varies jointly as the square of \(x\) the cube of \(z\) and the square root of \(W\). When \(x=1, z=2\), and \(w=36,\) then \(y=48\).

For the following exercises, find the inverse of the functions. $$ f(x)=9+2 \sqrt[3]{x} $$