Which of the following statements is true about the graph of \( f(x) = \frac{1}{x} \)?

Subtract the following rational expressions: \[\frac{x^2 + 5x}{x + 3} – \frac{x}{x + 3}\]

What is the multiplicity of the zero at \( x = -1 \)? The x-axis spans from below 0 to above 1, and the y-axis spans from below negative 5 to above 0. The x-axis has a scale of 1 in increments of 0.2 and the y-axis has a scale of 5 in increments of 1. The purple function has multiple turning points: it starts from negative infinity in the third quadrant, rises to a local maximum near the origin (0, 0), dips into a local minimum slightly below the point (0.5, negative 1) in the fourth quadrant, increases again to another local maximum around (1, 0), and then falls steeply towards negative infinity. The curve is symmetrical around vertical line passing through the local minimum.

What is the product of \( (x^2 + 1)(x + 3) \)?

What does the graph’s end behavior suggest about its leading coefficient? 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.

Simplify the product: \[\frac{x^2 – 25}{x^2 – 5x} \times \frac{x}{x – 5}\]

Which are factors of the polynomial shown in the graph? The x-axis spans from below negative 4 to 4, and the y-axis spans from below 0 to above 40. The x-axis has a scale of 2 in increments of 0.5 and the y-axis has a scale of 20 in increments of 5. The purple curve represents a polynomial function with three turning points. It starts from the bottom left of the third quadrant, rises to a local maximum near (negative 3, 45), decreases to a local minimum around the origin (0, 0). It rises again to another local maximum at a coordinate with x value roughly halfway between 1 and 1.5 and y value roughly between 5 and 10 and then decreases sharply as x increases.

What are the \( x \)-intercepts of the graph? 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.  

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

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