Chapter 5

For the following exercises, identify the function as a power function, a polynomial function, or neither. $$ -3 x $$

For the following exercises, use long division to divide. Specify the quotient and the remainder. $$ \left(x^{3}-3 x^{2}+5 x-6\right) \div(x-2) $$

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

For the following exercises, rewrite the quadratic functions in standard form and give the vertex. $$ f(x)=2 x^{2}-6 x $$

Find the degree and leading coefficient for the given polynomial. $$-3 x$$

For the following exercises, write an equation describing the relationship of the given variables. \(y\) varies inversely as the fourth power of \(x\) and when \(x=3, y=1\).

For the following exercises, find the domain, vertical asymptotes, and horizontes of the functions. $$ f(x)=\frac{x}{x^{2}+5 x-36} $$

For the following exercises, find the inverse of the functions. $$ f(x)=3 x^{3}+1 $$

For the following exercises, use the Remainder Theorem to find the remainder. $$ \left(4 x^{3}+5 x^{2}-2 x+7\right) \div(x+2) $$

For the following exercises, identify the function as a power function, a polynomial function, or neither. $$ 7-2 x^{2} $$

For the following exercises, use long division to divide. Specify the quotient and the remainder. $$ \left(2 x^{3}+3 x^{2}-4 x+15\right) \div(x+3) $$

For the following exercises, find the \(x\) - or \(t\) -intercepts of the polynomial functions. $$ f(x)=x^{3}+x^{2}-20 x $$

For the following exercises, rewrite the quadratic functions in standard form and give the vertex. $$ f(x)=3 x^{2}-5 x-1 $$

Find the degree and leading coefficient for the given polynomial. $$7-2 x^{2}$$

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 \(x=25, y=3\).

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

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

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

For the following exercises, identify the function as a power function, a polynomial function, or neither. $$ -2 x^{2}-3 x^{5}+x-6 $$

For the following exercises, use synthetic division to find the quotient. $$ \left(3 x^{3}-2 x^{2}+x-4\right) \div(x+3) $$

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

Find the degree and leading coefficient for the given polynomial. $$-2 x^{2}-3 x^{5}+x-6$$

For the following exercises, determine where 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 \(x=64, y=5\).

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

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

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

For the following exercises, identify the function as a power function, a polynomial function, or neither. $$ x\left(4-x^{2}\right)(2 x+1) $$

For the following exercises, use synthetic division to find the quotient. $$ \left(2 x^{3}-6 x^{2}-7 x+6\right) \div(x-4) $$

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

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

For the following exercises, determine where 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 \(z=3, y=36\).

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

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

For the following exercises, identify the function as a power function, a polynomial function, or neither. $$ x^{2}(2 x-3)^{2} $$

For the following exercises, use synthetic division to find the quotient. $$ \left(6 x^{3}-10 x^{2}-7 x-15\right) \div(x+1) $$

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

Find the degree and leading coefficient for the given polynomial. $$x^{2}(2 x-3)^{2}$$

For the following exercises, determine where 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 \(x=1, z=2,\) \(w=5,\) then \(y=100\).

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

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

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

For the following exercises, use synthetic division to find the quotient. $$ \left(4 x^{3}-12 x^{2}-5 x-1\right) \div(2 x+1) $$