Questions: ChatGPT ALEKS - Mariam Makar - Lear 5663 www-awy.aleks.com/alekscgi/x/lsl.exe/10u-IgNsIkr7j8P3jH-IJxKPnLS Rational Expressions Transforming the graph of a rational function Below is the graph of (y=frac1x). Transform it to make the graph of (y=frac1x+2-4).

$ChatGPT ALEKS - Mariam Makar - Lear 5663 www-awy.aleks.com/alekscgi/x/lsl.exe/10u-IgNsIkr7j8P3jH-IJxKPnLS Rational Expressions Transforming the graph of a rational function Below is the graph of (y=frac1x). Transform it to make the graph of (y=frac1x+2-4).$

Transcript text: ChatGPT ALEKS - Mariam Makar - Lear 5663 www-awy.aleks.com/alekscgi/x/lsl.exe/10_u-IgNsIkr7j8P3jH-IJxKPnLS Rational Expressions Transforming the graph of a rational function Below is the graph of $y=\frac{1}{x}$. Transform it to make the graph of $y=\frac{1}{x+2}-4$. Explanation Check

Solution

Solution Steps

Step 1: Horizontal Shift

The graph of $y = \frac{1}{x+2}$ is a horizontal shift of the graph $y = \frac{1}{x}$ two units to the left. This is because the addition of 2 to x shifts the graph in the negative x direction.

Step 2: Vertical Shift

The graph of $y = \frac{1}{x+2} - 4$ is a vertical shift of the graph $y = \frac{1}{x+2}$ four units down. This occurs because 4 is subtracted from the function.

Step 3: Combining the Transformations

To obtain the graph of $y = \frac{1}{x+2} - 4$ from $y = \frac{1}{x}$, we shift the graph of $y = \frac{1}{x}$ two units to the left and four units down. The vertical asymptote will be at $x = -2$ and the horizontal asymptote will be at $y = -4$.