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

If \( x^2 + 1 = 0 \), what are the roots?

If \( f(x) \) is multiplied by \( -k \), where \( k > 0 \), how does the graph change?

What is the degree of the polynomial function based on the end behavior? The x-axis spans from negative 4 to beyond 2, and the y-axis spans from below negative 5 to 10. The x-axis has a scale of 2 in increments of 0.5 and the y-axis has a scale of 5 in increments of 1. The green polynomial function has a local minimum at (negative 2, 0) and a local maximum at (0, 8). The function decreases from the top left of the second quadrant, reaching its minimum, then increases to its maximum on the y-axis before decreasing again, passing through the point (1, 0) and continuing into the fourth quadrant. The curve continues to extend out of view in both directions.

What is the result when \( (3x^3 + x) – (2x^3 + 4x) \) is simplified?

Which of the following points represents a valid solution to the constraints represented by the inequalities shown in the graph? The x-axis spans from negative 5 to 5, and the y-axis spans from below 0 to above 5. Both axes have a scale of 5 in increments of 1. A solid black inverted V-shaped function peak at (negative 1, 5). It opens downward with a y-intercept of (0, 4), an x-intercept of 4, 0), while enclosing a gray-shaded region below it. A dashed purple V-shaped function has a sharp vertex at (2, negative 1). It opens upward, with x-intercepts of (1, 0) and (3, 0), y-intercept of (0, 1), while enclosing a purple-shaded region above it. The two shaded areas overlap with intersection points (negative 2.5, 3.5) and (3.5, 0.5). The overlap forms a dark purple rectangular region at the center of the graph, spanning the first, second, and slight of the fourth quadrants.

Simplify the following: \[\frac{\frac{2x^2}{x + 3}}{\frac{x}{x – 3}}\]

What is the effect of the transformation \( f(x) = \frac{1}{x} \) to \( g(x) = \frac{1}{x} + 2 \)?

For the function \( f(x) = \frac{1}{x} \), replacing it with \( \frac{1}{x + 3} \) results in:

If \( f(x) = \vert x \vert \), what transformation is represented by \( g(x) = -\vert x – 2 \vert + 3 \)?