Describe the graph of y = 3 / (4x - 12) in comparison to the graph of y = 1 / x

Answer 1

The graph of y = 3 / (4x - 12) is a transformation of the graph of y = 1 / x.

The graph of y = 1 / x is a hyperbola with the x-axis as its horizontal asymptote and the y-axis as its vertical asymptote. It has branches in the first and third quadrants that extend outward and approach the x and y axes without ever touching them.

On the other hand, the graph of y = 3 / (4x - 12) is also a hyperbola, but it has been vertically stretched by a factor of 3 and horizontally compressed by a factor of 4. This means that the branches of the hyperbola are narrower and steeper compared to the original graph of y = 1 / x.

Additionally, the vertical asymptote of the transformed graph has shifted from x = 0 to x = 3, and the horizontal asymptote has shifted from y = 0 to y = 0. This means that the transformed graph is shifted to the right and up compared to the original graph.

Overall, the graph of y = 3 / (4x - 12) is a narrower, steeper, and shifted version of the graph of y = 1 / x.