Questions: Follow the seven step strategy to graph the following rational function. f(x) = x^4 / (x^2 + 13) 1. Select the symmetry of the function. - y-axis symmetry - origin symmetry - neither y-axis symmetry nor origin symmetry 2. Find the y-intercept. Select the correct choice below and fill in any answer boxes within your choice. A. The y-intercept is (Type an integer or a simplified fraction.) B. There is no y-intercept. 3. Find any x-intercepts. Select the correct choice below and fill in any answer boxes within your choice. A. The x-intercept(s) is/are (Type an integer or a simplified fraction. Use a comma to separate answers as needed.) B. There are no x-intercepts. 4. What are the x-coordinates of the vertical asymptote(s)? Select the correct choice below and fill in any answer boxes within your choice.

$Follow the seven step strategy to graph the following rational function. f(x) = x^4 / (x^2 + 13) 1. Select the symmetry of the function. - y-axis symmetry - origin symmetry - neither y-axis symmetry nor origin symmetry 2. Find the y-intercept. Select the correct choice below and fill in any answer boxes within your choice. A. The y-intercept is (Type an integer or a simplified fraction.) B. There is no y-intercept. 3. Find any x-intercepts. Select the correct choice below and fill in any answer boxes within your choice. A. The x-intercept(s) is/are (Type an integer or a simplified fraction. Use a comma to separate answers as needed.) B. There are no x-intercepts. 4. What are the x-coordinates of the vertical asymptote(s)? Select the correct choice below and fill in any answer boxes within your choice.$

Transcript text: Follow the seven step strategy to graph the following rational function. \[ f(x)=\frac{x^{4}}{x^{2}+13} \] 1. Select the symmetry of the function. $y$-axis symmetry origin symmetry neither $y$-axis symmetry nor origin symmetry 2. Find the $y$-intercept. Select the correct choice below and fill in any answer boxes within your choice. A. The $y$-intercept is $\square$ (Type an integer or a simplified fraction.) B. There is no $y$-intercept. 3. Find any $x$-intercepts. Select the correct choice below and fill in any answer boxes within your choice. A. The $x$-intercept(s) is/are $\square$ (Type an integer or a simplified fraction. Use a comma to separate answers as needed.) B. There are no $x$-intercepts. 4. What are the $x$-coordinates of the vertical asymptote(s)? Select the correct choice below and fill in any answer boxes within your choice.

Solution

Solution Steps

Step 1: Determine the Symmetry of the Function

The function $ f(x) = \frac{x^4}{x^2 + 13} $ is neither even nor odd. Therefore, it has neither $ y $-axis symmetry nor origin symmetry.

Step 2: Find the $ y $-Intercept

To find the $ y $-intercept, evaluate $ f(x) $ at $ x = 0 $: \[ f(0) = \frac{0^4}{0^2 + 13} = 0 \] Thus, the $ y $-intercept is 0.

Step 3: Find the $ x $-Intercepts

To find the $ x $-intercepts, set the numerator equal to zero and solve for $ x $: \[ x^4 = 0 \implies x = 0 \] Thus, the $ x $-intercept is 0.

Final Answer

Neither $ y $-axis symmetry nor origin symmetry.
The $ y $-intercept is 0.
The $ x $-intercept is 0.

{"axisType": 3, "coordSystem": {"xmin": -10, "xmax": 10, "ymin": -10, "ymax": 10}, "commands": ["y = (x4)/(x2 + 13)"], "latex_expressions": ["$y = \\frac{x^4}{x^2 + 13}$"]}

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