Question
Describe the transformation from v(x)=x−1−−−−√+4
to q(x)=0.5(x−1)−−−−−−−−√+4
.(1 point)
Responses
horizontal compression by a factor of 0.5
horizontal compression by a factor of 0.5
horizontal stretch by a factor of 0.5
horizontal stretch by a factor of 0.5
horizontal stretch by a factor of 2
horizontal stretch by a factor of 2
horizontal compression by a factor of 2
to q(x)=0.5(x−1)−−−−−−−−√+4
.(1 point)
Responses
horizontal compression by a factor of 0.5
horizontal compression by a factor of 0.5
horizontal stretch by a factor of 0.5
horizontal stretch by a factor of 0.5
horizontal stretch by a factor of 2
horizontal stretch by a factor of 2
horizontal compression by a factor of 2
Answers
Answered by
GPT-4o mini
To analyze the transformation from the function \( v(x) = \sqrt{x - 1} + 4 \) to the function \( q(x) = 0.5 \sqrt{x - 1} + 4 \), we need to look at how the transformation affects the shape and dimensions of the graph.
1. The expression \( \sqrt{x - 1} \) remains the same in both functions, which means the basic shape of the graph does not experience vertical shifts or alterations in shape.
2. The key difference is the multiplication factor of 0.5 in \( 0.5 \sqrt{x - 1} + 4 \). This factor scales the output of \( \sqrt{x - 1} \) vertically. However, we're specifically interested in the transformation of \( x \) itself.
In terms of \( x \):
- The transformation \( \sqrt{0.5(x - 1)} \) can be rewritten as \( \sqrt{x - 1} \) and undergone a horizontal transformation. A multiplication of 0.5 inside the square root indicates a horizontal stretch because it spreads the graph along the x-axis.
Thus, the proper description for the transformation from \( v(x) \) to \( q(x) \) is that it represents a **horizontal stretch by a factor of 2**.
In summary, the correct response is:
**horizontal stretch by a factor of 2**.
1. The expression \( \sqrt{x - 1} \) remains the same in both functions, which means the basic shape of the graph does not experience vertical shifts or alterations in shape.
2. The key difference is the multiplication factor of 0.5 in \( 0.5 \sqrt{x - 1} + 4 \). This factor scales the output of \( \sqrt{x - 1} \) vertically. However, we're specifically interested in the transformation of \( x \) itself.
In terms of \( x \):
- The transformation \( \sqrt{0.5(x - 1)} \) can be rewritten as \( \sqrt{x - 1} \) and undergone a horizontal transformation. A multiplication of 0.5 inside the square root indicates a horizontal stretch because it spreads the graph along the x-axis.
Thus, the proper description for the transformation from \( v(x) \) to \( q(x) \) is that it represents a **horizontal stretch by a factor of 2**.
In summary, the correct response is:
**horizontal stretch by a factor of 2**.