The line y = x is transformed to create the line
y
=
−
1
2
x
−
1
. Which of the following may be used to describe the transformation? Select all that apply.
A.
All x-values are opposites of half the original x-values.
B.
The graph is reflected across the y-axis, moved 1 unit down, and the rate of change is halved.
C.
All x-values are half the original x-values.
D.
The graph is reflected across the y-axis, moved 1 unit down, and the rate of change is doubled.
?my answer is A and B
To determine which of the options may be used to describe the transformation of the line y = x to y = -1/2x - 1, we can analyze the changes that occurred.
1. Option A states that all x-values are opposites of half the original x-values. This is not true because the x-values in the new equation are not opposites of the original x-values. Therefore, option A is incorrect.
2. Option B states that the graph is reflected across the y-axis, moved 1 unit down, and the rate of change is halved. This is correct. The graph is indeed reflected across the y-axis (due to the negative sign in front of the x), moved 1 unit down (due to the constant term -1), and the rate of change is halved (the coefficient of x is -1/2 compared to the original coefficient of 1). Therefore, option B is correct.
3. Option C states that all x-values are half the original x-values. This is not true because the x-values in the new equation are not half the original x-values. Therefore, option C is incorrect.
4. Option D states that the graph is reflected across the y-axis, moved 1 unit down, and the rate of change is doubled. This is not true. The rate of change in the new equation is halved (-1/2) compared to the original rate of change (1). Therefore, option D is incorrect.
Based on the analysis, you are correct. The correct options that may be used to describe the transformation are B (the graph is reflected across the y-axis, moved 1 unit down, and the rate of change is halved).
ever try just typing things on one line?
If you meant y = -1/2 x - 1
then B