When the graph of \( f(x) = \frac{1}{x} \) is reflected across the y-axis, what is the resulting function?

What is the effect of the negative sign in \( f(x) = -\frac{1}{x + 4} \)? The x-axis spans from below negative 6 to 2, and the y-axis spans from below negative 10 to above 10. The x-axis has a scale of 2 in increments of 0.5, and the y-axis has a scale of 10 in increments of 2. The function has a vertical asymptote at x= negative 4 and a horizontal asymptote at y = 0. The convex curve is in the second quadrant, passing through the points (negative 4.25, 4) and (negative 5, 1). The curve starts from positive infinity above the vertical asymptote near x= negative 4, then decreases sharply approaching the horizontal asymptote near y = 0. The concave curve spans the third and the fourth quadrants, passing through the approximate points (negative 3.75, negative 4) and (negative 3, negative 1). It starts from negative infinity approaching the vertical asymptote near x= negative 2, then rises steeply approaching the horizontal asymptote near y = 0.

Match the transformation with the function representation for each transformation applied to the graph of as shown in the graph. The x-axis spans from negative 5 to above 5, and the y-axis spans from below negative 5 to above 5. Both axes have a scale of 5 in increments of 1. The purple V-shaped function consists of two linear segments meeting at a sharp vertex at the coordinate (2, negative 5). The left segment has a negative slope, with y-intercept of (0, 1), and x-intercept roughly located halfway between (0, 0) and (1, 0). The right segment has a positive slope, passing through the coordinate roughly located halfway between (3, 0) and (4, 0)

How does the graph of \( f(x) \) change when it becomes \( -2 \cdot f(x) \)?

What are the asymptotes of the function \( f(x) = \frac{3x}{x^2 – 4} \)?

Simplify the complex fraction: \[\frac{\frac{x^2 + 2x}{x^2 – 4}}{\frac{x}{x – 2}}\]

What are the vertical asymptotes of \[f(x) = \frac{x + 1}{x^2 – 2}?\] “The x-axis spans from below negative 4 to just above 4, and the y-axis spans from below negative 10 to just above 10. The x-axis has a scale of 2 in increments of 0.5, and the y-axis has a scale of 10 in increments of 2. The leftmost branch is a sharp concave curve in the third quadrant, starting from negative infinity near x = negative 1.5, increasing steeply, and then abruptly approaching the horizontal asymptote near y = 0.  The middle branch is between the asymptotes, decreasing from positive infinity near x = negative 1.5 in the second quadrant, passing through the point (negative 1,0) in a flat pattern and continuing downward past negative infinity near x = 1.5 in the fourth quadrant.   The rightmost branch is a sharp convex curve in the first quadrant, starting from positive infinity near x= 1.5 and decreasing steeply before leveling off as it approaches the horizontal asymptote near y= 0.  “

What is the x-intercept of \( f(x) = \frac{x}{x^2 – 1} \)?

Subtract the following rational expressions: \[\frac{x^2}{x + 1} – \frac{2x}{x – 1}\]

Simplify \( (4 + 2i) – (1 – 3i) \).