Which of the following rational functions have a vertical asymptote at \( x = 3 \)?

Identify the horizontal asymptote for the rational function \( f(x) = \frac{4x + 3}{2x + 5} \).

Solve \( x^2 + 4 = 0 \).

What is the y-intercept of \[f(x) = \frac{5x}{x + 2}?\] The x-axis spans from below negative 10 to just above 5, and the y-axis spans from just below negative 20 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 convex curve is in the second quadrant, passing through the points (negative 3, 15) and (negative 6, 7.5). The curve starts from positive infinity above the vertical asymptote near x= negative 2, then decreases, approaching the horizontal asymptote near y = 5. The concave curve spans the third and the first quadrants, passing through the approximate points (negative 1.5, negative 15) and (3, 2.5). It starts from negative infinity approaching the vertical asymptote near x= negative 2, then rises approaching the horizontal asymptote near y = 5. 

Rewrite the equation in standard form and identify the conic:   \(x^2 + y^2 – 12x – 4y + 7 = 0\)

What are the approximate coordinates of the local minimum? The x-axis spans from negative 10 to 10, and the y-axis spans from below negative 100 to above 200. The x-axis has a scale of 5 in increments of 1 and the y-axis has a scale of 100 in increments of 20. The red curve represents a polynomial function with four turning points. It starts from the bottom left of the third quadrant and rises sharply to a local maximum near (negative 3.5, 200). It then decreases to a local minimum to a coordinate with x values roughly halfway between 0 and negative 1 and y value halfway between negative 140 and negative 150. It rises again to another local maximum around (2, 70), decreases to another local minimum near (4, negative 150), and then increases steeply toward positive infinity.

Which of the following describes the behavior at \( x = -1 \)? The x-axis spans from below zero to 5, and the y-axis spans from just below 0 to above 20. Both axes have a scale of 5 with grid lines in increments of 1. The green polynomial function has two local minima and one local maximum. It starts from positive infinity in the second quadrant, decreases to a local minimum at (negative 1, 0), rises to a local maximum at (1, 16), and then falls to another local minimum at (3, 0) before increasing towards positive infinity in the first quadrant.  

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

Which of the following is the equation of the horizontal asymptote for \[f(x) = \frac{x^2 + 3}{x^2 – 1}?\]

The graph of \( f(x) = \frac{1}{x} \) is transformed into \( f(x) = \frac{1}{2x} \). What happens to the graph?