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Author Archives: Anonymous

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

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

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

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

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If \( f(x) \) is multiplied by \( -k \), where \( k > 0 \),…

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

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What is the degree of the polynomial function based on the e…

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.

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What is the result when \( (3x^3 + x) – (2x^3 + 4x) \) is si…

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

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Which of the following points represents a valid solution to…

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.

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

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

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What is the effect of the transformation \( f(x) = \frac{1}{…

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

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For the function \( f(x) = \frac{1}{x} \), replacing it with…

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

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If \( f(x) = \vert x \vert \), what transformation is repres…

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

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