The polynomial function \( f(x)=x^{3}-9 x \) is multiplied by \( \frac{-1}{3} \) to produce the function \( g(x)=-\frac{1}{3} x^{3}+3 x \). Which of the following is true about the \( [ \) Window] settings for the graph of \( g(x) \) ? A Multiply the \( X_{\min \text { and }} X_{\max } \) from \( f(x) \) by \( -\frac{1}{3} \). B Multiply the \( Y_{\min \text { and }} Y_{\max } \) from \( f(x) \) by \( -\frac{1}{3} \). C Multiply the \( X_{\min ,} X_{\max }, Y_{\min } \), and \( Y_{\max } \) from \( f(x) \) by \( -\frac{1}{3} \). D Keep the settings from \( f(x) \).

List the domain and the \( x \)-and \( y \)-intercepts of the following function. Graph the function. \( f(x)=\frac{5}{x} \)

The function \( f(x)=x^{3}-5 \) is one-to-one. (a) Find the inverse of \( f \) and check the answer. (b) Find the domain and the range of \( f \) and \( { }^{-1} \) (c) Graph \( f, f^{-1} \), and \( y=x \) on the same coordinate axes. (a) \( f^{-1}(x)=\sqrt[3]{x+5} \) (Simplify your answer. Use integers or fractions for any numbers in the expression.) (b) Find the domain of \( f \). Select the correct choice below and, if necessary, fill in the answer box to o B. The domain is \( \{x \mid x \neq \square \). C. The domain is \( \{x \mid x \leq\} \). D. The domain is the set of all real numbers. ( \( 4 x \mid x \geq\} \).

Jse transformations to graph the function. Determine the domain, range, horizontal asymptote, and \( y \)-intercept of the function. \( (x)=3+5^{x-1} \) Use the graphing tool to graph the function. What is the domain of \( f(x)=3+5^{x-1} \) ? (Type your answer in interval notation.)

Begin with the graph of \( y=e^{x} \). Use transformations to graph the function below. Then determine its domain, range, and horizontal asymptote. \( f(x)=-8-e^{-x} \) Use the graphing tool to graph the function. (For any answer boxes shown with the grapher, type an exact answer.) What is the domain of \( f(x)=-8-e^{-x} \) ? (Type your answer in interval notation.)

Sketch the graph of a polynomial function with roots at \( 2 \) (multiplicity 1), \( -3 \) (multiplicity 2), and \( 4 \) (multiplicity 3). Describe how each root affects the shape of the graph.