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 \( (4 + 2i) – (1 – 3i) \).

Subtract the rational expressions: \[\frac{x + 2}{x^2 + 3x + 2} – \frac{1}{x^2 + 3x + 2}\]

For \[f(x) = \frac{2x}{x – 3},\] what is the vertical asymptote? The x-axis spans from below zero to above 5, and the y-axis spans from below negative 10 to above 10. The x-axis has a scale of 5 in increments of 1, and the y-axis has a scale of 10 in increments of 2. The convex curve is in the first quadrant, passing through the points (3.5, 14) and (6,4). It starts from positive infinity above the vertical asymptote near x= 3. It decreases steeply before leveling off as it approaches the horizontal asymptote near y= 1. The concave curve spans the fourth, and second quadrants, passing through (2, negative 4) and the point slightly below (negative 2, 1). It starts from negative infinity below the vertical asymptote near x= 3, increasing steeply, and then approaching the horizontal asymptote near y =1 in the second quadrant after passing through the origin (0,0).