For the function \( f(x) = \frac{1}{x} – 2 \), the horizontal asymptote is at:

What is the horizontal asymptote of \( f(x) = \frac{5x}{x + 2} \)?

What is the minimum value of the polynomial function? The x-axis spans from below negative 5 to above 5, and the y-axis spans from below negative 20 to 10. 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 blue parabola opens upward, with its vertex at approximately (negative 0.5, negative 20). The curve is symmetric around the vertical line passing through the vertex. It intersects the y-axis at (0, negative 20). It crosses the x-axis at (negative 5, 0) and (4, 0), extending out of view at both ends. 

If \( y = \frac{12}{x} \), which of the following is true about the graph?

Identify the removable discontinuity of \[f(x) = \frac{(x – 2)(x + 1)}{(x – 2)(x – 3)}\]

For \[f(x) = \frac{5x}{x^2 – 9},\] which is a vertical asymptote of the function?

The function is \( y = \frac{10}{x^2 – 9} \). Which statement is true about the vertical asymptotes? The x-axis spans from just below negative 5 to above 5, and the y-axis spans from below negative 20 to just 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 and a wide bounded region between x = negative 3 and x = 3. The left convex curve starts from positive infinity above the vertical asymptote, decreases toward the negative x-axis, and extends horizontally. The right convex curve starts from positive infinity decreases, and flattens toward the positive x-axis. The middle inverted U-shaped curve gradually declines at both sides from approximately (0, negative 2), passes through the points (negative 2.5, negative 2.5) and (2.5, negative 2.5) respectively, then descends steeply toward negative infinities. 

Simplify the product: \[\frac{3x + 6}{x^2 + 3x} \times \frac{x + 3}{x + 2}\]

Which value is a multiple root of the polynomial shown in the graph have? The x-axis spans from negative 10 to 10, and the y-axis spans from below 0 to above 40. 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 polynomial function has a local minimum around (negative 3, 0) and a local maximum near (1.5, 50). The function starts from positive infinity, decreases to the local minimum, rises to the local maximum, and then falls towards negative infinity, extending out of view at both ends.

What is the effect of adding 3 to the reciprocal function \( f(x) = \frac{1}{x} \)?