Summarize the pertinent information obtained by applying the graphing strategy and sketch the graph of \( y=f(x) \). \( f(x)=18 x(x-1)^{3} \) What is the domain of the function? Select the correct choice below and, if necessary, fill in the answer box to complete your choice. The domain is \( \square \). (Type your answer in interval notation. Use a comma to separate answers as needed.) What is the \( y \)-intercept? Select the correct choice below and, if necessary, fill in the answer box to complete your choice. A. The \( y \)-intercept is \( y=\square \). There is no \( y \)-intercept. What is/are the \( x \)-intercept(s)? Select the correct choice below and, if necessary, fill in the answer box to complete your choice. A. The \( x \)-intercept(s) is/are \( x=\square \). (Simplify your answer. Use a comma to separate answers as needed.) B. There is no \( x \)-intercept.

**Domain** Since \( f(x)=18x(x-1)^3 \) is a polynomial (which is defined for all real numbers), the domain is \[ (-\infty, \infty). \] **\( y \)-Intercept** To find the \( y \)-intercept, set \( x=0 \): \[ f(0)=18(0)(0-1)^3=0. \] Thus, the \( y \)-intercept is at \[ y=0. \] **\( x \)-Intercept(s)** To find the \( x \)-intercepts, set \( f(x)=0 \): \[ 18x(x-1)^3=0. \] This equation holds when either \[ x=0 \quad \text{or} \quad (x-1)^3=0. \] Solving \( (x-1)^3=0 \) gives \[ x=1. \] Thus, the \( x \)-intercepts are at \[ x=0 \quad \text{and} \quad x=1. \] **Graph Sketch Summary** - The graph is a polynomial curve. - It has a \( y \)-intercept at \( (0,0) \). - It crosses the \( x \)-axis at \( x=0 \) and touches/crosses the \( x \)-axis at \( x=1 \) with a multiplicity of 3 (indicating a point of inflection or flattening behavior at \( x=1 \)). - The function is defined for all \( x \in \mathbb{R} \). **Final Answers** - **Domain:** \( (-\infty, \infty) \) - **\( y \)-Intercept:** \( y=0 \) - **\( x \)-Intercept(s):** \( x=0, \, 1 \)