Multiply and simplify: \[\frac{x^2 + 2x}{x^2 – 9} \times \frac{x – 3}{x + 2}\]

Which are factors of the polynomial shown?  The x-axis spans from below negative 4 to 4, and the y-axis spans from below 0 to above 40. The x-axis has a scale of 2 in increments of 0.5 and the y-axis has a scale of 20 in increments of 5. The purple curve represents a polynomial function with three turning points. It starts from the bottom left of the third quadrant, rises to a local maximum near (negative 3, 45), decreases to a local minimum around the origin (0, 0). It rises again to another local maximum at a coordinate with x value roughly halfway between 1 and 1.5 and y value roughly between 5 and 10 and then decreases sharply as x increases.

What are the zeros of the polynomial shown in the graph? The x-axis spans from negative 4 to 4, 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 orange polynomial function has an inflection point around the origin (0,0), with a local maximum at approximately (negative 0.5, 1) and a local minimum near (1.25, negative 2). The function decreases from negative infinity, rises to the local maximum, falls to the local minimum, and then increases towards positive infinity, extending out of view at both ends. 

What happens to the graph of \( f(x) \) when it is replaced with \( f(x – k) \) for \( k > 0 \)?

If \( P(x) = x^3 – 4x^2 + 5x – 2 \), which of the following are NOT a possible rational root?

Which of the following steps is correct to graph \[f(x) = \frac{x}{x^2 – 9}?\]

Multiply \( (x^2 – 3)(x + 5) \):

Simplify: \[\frac{x}{x^2 – 1} + \frac{1}{x + 1}\]

Which of the following represents the factorization of \( x^3 – 3x^2 – 4x + 12 \)?

The function is \( y = \frac{6}{x^2 – x} \). Which is a vertical asymptote of this function? The x-axis spans from below negative 5 to beyond 5, and the y-axis spans from below negative 40 to above 20. The x-axis has a scale of 5 in increments of 1, and the y-axis has a scale of 20 in increments of 5. The red rational function consists of two convex curves in the first and second quadrants, with a narrow, bounded region with single peak below the x-axis. The first-quadrant convex curve starts from positive infinity near the vertical line x = 1, decreases sharply, and then approaches the horizontal asymptote along the positive x-axis. The second quadrant convex curve starts from positive infinity near x = 0, decreases toward the negative x-axis, and extends horizontally. A single narrow peak appears in the fourth quadrant near the point (0.5, negative 24), where the function briefly rises before decreasing again. This localized fluctuation is confined to a narrow, bounded region in between x = 0 and x = 1.