Which equation represents a vertical compression of \( f(x) = \vert x \vert \) by a factor of \( \frac{1}{4} \)?

When two quantities are inversely proportional, which statement is true?

Use long division to simplify \( (x^3 + 2x^2 – 3x – 6) \div (x + 2) \). What is the quotient?

Which of the following statements about the graph of \( f(x) = \frac{x}{x^2 – 1} \) is correct?

If \( f(x) = \frac{1}{x} \) is transformed to \( g(x) = \frac{1}{x} – 3 \), what happens to the graph?

The graph of \( f(x) = \frac{1}{x^2} \) differs from \( f(x) = \frac{1}{x} \) in which way?

Add the rational expressions: \[\frac{2}{x^2 + 5x + 6} + \frac{x}{x^2 + 5x + 6}\]

Which value is a valid solution to the system shown? “The x-axis spans from below zero to 6, and the y-axis spans from negative 4 to 4. Both axes have a scale of 2 in increments of 0.5. A dashed black parabola opens upward, enclosing a gray-shaded parabolic region above it. The vertex of this parabola is at (3, negative 1), while it passes through the x-axis at (2, 0) and (4, 0). Another solid green parabola opens downward and encloses a light green parabolic region below it. The vertex of this parabola is at (2, 1), while it passes through the x-axis at (1, 0) and (3, 0). The two parabolic regions overlap, forming a dark green-gray region in the middle of the graph where the two curves intersect at approximately (1.6, 0.9) and again at approximately (3.8, -0.8)”

For the function \( f(x) = \frac{1}{x} \), replacing \( x \) with \( 2x \) results in:

What is the degree of the polynomial function based on the end behavior? The x-axis spans from negative 2 to 6, and the y-axis spans from below negative 10 to above 5. 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 around (1, negative 4) and a local maximum around (3, 0). The function starts from positive infinity in the second quadrant, decreases to the local minimum in the fourth quadrant, rises to the local maximum, and then falls again towards negative infinity, extending out of view at both ends.