Chapter 5

Identify the function as a power function, a polynomial function, or neither. $$f(x)=x^{5}$$

For the following exercises, write an equation describing the relationship of the given variables. \(y\) varies directly as the cube of \(x\) and when \(x=36, y=24\).

For the following exercises, find the domain of the rational functions. $$ f(x)=\frac{x+1}{x^{2}-1} $$

For the following exercises, find the inverse of the function on the given domain. $$ f(x)=(x+1)^{2}-3,[-1, \infty) $$

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

For the following exercises, identify the function as a power function, a polynomial function, or neither. $$ f(x)=\left(x^{2}\right)^{3} $$

For the following exercises, use long division to divide. Specify the quotient and the remainder. $$ \left(6 x^{2}-25 x-25\right) \div(6 x+5) $$

For the following exercises, find the \(x\) - or \(t\) -intercepts of the polynomial functions. $$ C(t)=3(t+2)(t-3)(t+5) $$

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

Identify the function as a power function, a polynomial function, or neither. $$f(x)=\left(x^{2}\right)^{3}$$

For the following exercises, write an equation describing the relationship of the given variables. \(y\) varies directly as the cube root of \(x\) and when \(x=27, y=15\).

For the following exercises, find the domain of the rational functions. $$ f(x)=\frac{x^{2}+4}{x^{2}-2 x-8} $$

For the following exercises, find the inverse of the function on the given domain. $$ f(x)=3 x^{2}+5,(-\infty, 0] $$

For the following exercises, use the Remainder Theorem to find the remainder. $$ \left(x^{4}+5 x^{3}-4 x-17\right) \div(x+1) $$

For the following exercises, identify the function as a power function, a polynomial function, or neither. $$ f(x)=x-x^{4} $$

For the following exercises, use long division to divide. Specify the quotient and the remainder. $$ \left(-x^{2}-1\right) \div(x+1) $$

For the following exercises, find the \(x\) - or \(t\) -intercepts of the polynomial functions. $$ C(t)=4 t(t-2)^{2}(t+1) $$

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

Identify the function as a power function, a polynomial function, or neither. $$f(x)=x-x^{4}$$

For the following exercises, write an equation describing the relationship of the given variables. \(y\) varies directly as the fourth power of \(x\) and when \(x=1\) \(y=6\).

For the following exercises, find the domain of the rational functions. $$ f(x)=\frac{x^{2}+4 x-3}{x^{4}-5 x^{2}+4} $$

For the following exercises, find the inverse of the function on the given domain. $$ f(x)=12-x^{2},[0, \infty) $$

For the following exercises, use the Remainder Theorem to find the remainder. $$ \left(-3 x^{2}+6 x+24\right) \div(x-4) $$

For the following exercises, identify the function as a power function, a polynomial function, or neither. $$ f(x)=\frac{x^{2}}{x^{2}-1} $$

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

For the following exercises, find the \(x\) - or \(t\) -intercepts of the polynomial functions. $$ C(t)=2 t(t-3)(t+1)^{2} $$

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

Identify the function as a power function, a polynomial function, or neither. $$f(x)=\frac{x^{2}}{x^{2}-1}$$

For the following exercises, write an equation describing the relationship of the given variables. \(y\) varies inversely as \(x\) and when \(x=4, y=2\).

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

For the following exercises, find the inverse of the function on the given domain. $$ f(x)=9-x^{2},[0, \infty) $$

For the following exercises, use the Remainder Theorem to find the remainder. $$ \left(5 x^{5}-4 x^{4}+3 x^{3}-2 x^{2}+x-1\right) \div(x+6) $$

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

For the following exercises, use long division to divide. Specify the quotient and the remainder. $$ \left(x^{3}-126\right) \div(x-5) $$

For the following exercises, find the \(x\) - or \(t\) -intercepts of the polynomial functions. $$ C(t)=2 t^{4}-8 t^{3}+6 t^{2} $$

For the following exercises, rewrite the quadratic functions in standard form and give the vertex. $$ h(x)=2 x^{2}+8 x-10 $$

Identify the function as a power function, a polynomial function, or neither. $$f(x)=2 x(x+2)(x-1)^{2}$$

For the following exercises, write an equation describing the relationship of the given variables. \(y\) varies inversely as the square of \(x\) and when \(x=3, y=2\).

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

For the following exercises, find the inverse of the function on the given domain. $$ f(x)=2 x^{2}+4,[0, \infty) $$

For the following exercises, use the Remainder Theorem to find the remainder. $$ \left(x^{4}-1\right) \div(x-4) $$

For the following exercises, identify the function as a power function, a polynomial function, or neither. $$ f(x)=3^{x+1} $$

For the following exercises, use long division to divide. Specify the quotient and the remainder. $$ \left(3 x^{2}-5 x+4\right) \div(3 x+1) $$

For the following exercises, find the \(x\) - or \(t\) -intercepts of the polynomial functions. $$ C(t)=4 t^{4}+12 t^{3}-40 t^{2} $$

For the following exercises, rewrite the quadratic functions in standard form and give the vertex. $$ k(x)=3 x^{2}-6 x-9 $$

Identify the function as a power function, a polynomial function, or neither. $$f(x)=3^{x+1}$$

For the following exercises, write an equation describing the relationship of the given variables. \(y\) varies inversely as the cube of \(x\) and when \(x=2, y=5\).

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

For the following exercises, find the inverse of the functions. $$ f(x)=x^{3}+5 $$

For the following exercises, use the Remainder Theorem to find the remainder. $$ \left(3 x^{3}+4 x^{2}-8 x+2\right) \div(x-3) $$