Follow the seven step strategy to graph the following rational function. f(x)=(5x)/(x-4) origin symmetry neither y-axis symmetry nor origin symmetry What is the y-intercept?Select the correct choice below and, if necessary fill in the answer box to complete your choi A.The y-intercept is 0 (Type an integer or a simplified fraction.) B. 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 you A. The x-intercept(())is/are 0. (Type an integer or a simplified fraction. Use a comma to separate answers as needed.) B. There is no x-intercept Find the vertical asymptote(s)Select the correct choice below and, if necessary,fill in the answer box to complete you A. The equation(s) of the vertical asymptote(s) is/are square (Type an equation. Use a comma to separate answers as needed.) C B. There is no vertical asymptote.

To graph the rational function \( f(x) = \frac{5x}{x-4} \), we will follow a seven-step strategy. Let's go through each step:<br /><br />1. **Determine Symmetry:**<br /> - **Y-axis symmetry:** A function is symmetric about the y-axis if \( f(-x) = f(x) \). For this function, \( f(-x) = \frac{5(-x)}{-x-4} = \frac{-5x}{-x-4} \neq \frac{5x}{x-4} \), so it is not symmetric about the y-axis.<br /> - **Origin symmetry:** A function is symmetric about the origin if \( f(-x) = -f(x) \). Here, \( f(-x) = \frac{-5x}{-x-4} \) and \( -f(x) = -\frac{5x}{x-4} \). These are not equal, so the function does not have origin symmetry.<br /><br />2. **Find the Y-intercept:**<br /> - The y-intercept occurs when \( x = 0 \). Substitute \( x = 0 \) into the function:<br /> \[<br /> f(0) = \frac{5(0)}{0-4} = 0<br /> \]<br /> - So, the y-intercept is 0. The correct choice is:<br /> - A. The \( y \)-intercept is 0.<br /><br />3. **Find the X-intercept(s):**<br /> - The x-intercept(s) occur when \( f(x) = 0 \). Set the numerator equal to zero:<br /> \[<br /> 5x = 0 \implies x = 0<br /> \]<br /> - So, the x-intercept is 0. The correct choice is:<br /> - A. The \( x \)-intercept(s) is/are 0.<br /><br />4. **Find Vertical Asymptote(s):**<br /> - Vertical asymptotes occur where the denominator is zero (and the numerator is not zero at those points). Set the denominator equal to zero:<br /> \[<br /> x - 4 = 0 \implies x = 4<br /> \]<br /> - So, there is a vertical asymptote at \( x = 4 \). The correct choice is:<br /> - A. The equation(s) of the vertical asymptote(s) is/are \( x = 4 \).<br /><br />5. **Find Horizontal Asymptote(s):**<br /> - For rational functions where the degree of the numerator equals the degree of the denominator, the horizontal asymptote is given by the ratio of the leading coefficients. Here, both the numerator and denominator have degree 1, so the horizontal asymptote is:<br /> \[<br /> y = \frac{5}{1} = 5<br /> \]<br /><br />6. **Plot Additional Points:**<br /> - Choose additional values of \( x \) to plot points and get a better sense of the graph's shape. For example, calculate \( f(2) \), \( f(6) \), etc.<br /><br />7. **Sketch the Graph:**<br /> - Use the intercepts, asymptotes, and additional points to sketch the graph of the function. The graph should approach the vertical asymptote at \( x = 4 \) and the horizontal asymptote at \( y = 5 \).<br /><br />By following these steps, you can accurately graph the function \( f(x) = \frac{5x}{x-4} \).