2. How do the graphs of y = 1/x and y = 3/x – 4 compare? (1 point)
Compared to the graph of y = 1/x, the graph of y = 3/x – 4 is a vertical stretch by a factor of 3 and a translation of 4 units left.
Compared to the graph of y = 1/x, the graph of y = 3/x – 4 is a vertical shrink by a factor of 3 and a translation of 4 units up.
*Compared to the graph of y = 1/x, the graph of y = 3/x – 4 is a vertical stretch by a factor of 3 and a translation of 4 units down.
Compared to the graph of y = 1/x, the graph of y = 3/x – 4 is a vertical shrink by a factor of 3 and a translation of 4 units down.
I think it's C. I marked it with *.
Thank You.
Yes, your answer is correct. The correct option is C: "Compared to the graph of y = 1/x, the graph of y = 3/x – 4 is a vertical stretch by a factor of 3 and a translation of 4 units down."
To understand why this is the correct answer, we need to analyze the equations of the two graphs and how they differ from each other.
The graph of y = 1/x is a basic reciprocal function. It has a vertical asymptote at x = 0 (since you cannot divide by zero) and a horizontal asymptote at y = 0. The graph starts in the first quadrant and approaches the x and y axes as it extends.
When we introduce the equation y = 3/x – 4, this modifies the original reciprocal function. The "3/x" part causes a vertical stretch by a factor of 3. This means that the graph gets vertically stretched, making it narrower and taller compared to the original graph.
Then, the "– 4" part acts as a translation. Since it is subtracted from the function, it shifts the entire graph down by 4 units. This means that every point on the graph is moved downward by 4 units, resulting in a lower y-intercept and a downward shift of the whole graph.
Therefore, the graph of y = 3/x – 4 is a vertical stretch by a factor of 3 and a translation of 4 units down when compared to the original graph of y = 1/x.
Yes, you are correct. The correct answer is C.
Compared to the graph of y = 1/x, the graph of y = 3/x – 4 is a vertical stretch by a factor of 3 and a translation of 4 units down.
This means that the graph of y = 3/x – 4 will look similar to the graph of y = 1/x, but it will appear narrower/stretched vertically by a factor of 3, and it will be shifted 4 units downward.