Category: Uncategorized

If \( f(x) = \frac{1}{x} \), what is the result of replacing it with \( f(x) – 3 \)?

Which function has a hole at \( x = -1 \)?

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

For the rational function \[f(x) = \frac{1}{x^2 – 1},\] what are the equations of the vertical asymptotes?

Identify the simplified form of the following expression: \[\frac{x^2 + x – 6}{x^2 + 4x + 3}\]

What are the zeros of the polynomial represented in the graph? The x-axis spans from below negative 5 to 5, and the y-axis spans from below negative 20 to above zero. 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 red curve represents a polynomial function with four turning points. It begins from the bottom-middle of the third quadrant, reaches a local maximum at (negative 3, 0), then drops steeply to a local minimum near (negative 1.5, negative 21). It rises again to another local maximum near (0.5, 0.8), falls to a local minimum around (1, 0), and then steeply extends upward out of view. 

A delivery truck transports small packages (\( x \)) and large packages (\( y \)). Each small package weighs 10 lbs, and each large package weighs 30 lbs. The truck can carry a maximum of 500 lbs. Which inequality represents the weight constraint?

What is the degree of the polynomial \( 7x^6 – 2x^3 + x + 10 \)?

What is the zero of \( f(x) = \frac{x – 3}{x + 1} \)?

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