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Which system of inequalities represents the constraints shown in the graph? “Area graph. A gray-shaded area and a purple-shaded area intersect on a coordinate plane, forming a grayish purple area. The x-axis spans from negative 5 to just above 5, and the y-axis spans from below 0 to above 5. Both axes show intervals of 5 with grid lines in increments of 1. A solid black diagonal line with a negative slope has an x-intercept roughly halfway between (2, 0) and (3, 0) and a y-intercept at (0, 7), shading the area below in dark gray. A dashed purple diagonal line with a positive slope has an x-intercept at (negative 3, 0) and a y-intercept at (0, 3), shading the area above in light purple. The two shaded areas overlap, forming a grayish purple region. The overlapping area spans most of the second quadrant and some portion of the first and third quadrants.”

Which transformation occurs when \( g(x) = f(-x) \)?

What are the zeros of the polynomial shown in the graph? The x-axis spans from below negative 5 to above 5, and the y-axis spans from below negative10 to 20. 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 green parabola opens upward, with its vertex at approximately (0, negative 9). The curve is symmetric around the y-axis. It crosses the x-axis at (negative 3, 0) and (3, 0), extending out of view at both ends. 

If \( P(x) = 4x^2 – 12x + 9 \), what are the roots of \( P(x) \)?

Multiply the rational expressions and simplify: \[\frac{x^2 – 1}{2x + 4} \times \frac{x + 2}{x – 1}\]

Given \( f(x) = \frac{x + 1}{x – 4} \), what is the domain of the function?

Add and simplify: \[\frac{1}{x – 2} + \frac{1}{x + 2}\]

How many \( x \)-intercepts can the graph of \( f(x) = x^2 – 4 \) have?

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

When \( f(x) \) is replaced by \( -f(x) \), what is the effect on the graph?