the graph of y= -1/4 over x-2 can be obtained from the graph y|x| by which transformations?
a. 5 units to right
b. 2 units to right
c. 5 units to left
d. 2 units to left
by what factor is the graphed streched or shrunk vertically and how is it reflected.
a. shrunk verticallyby a factor of 1/4, reflected over the y-axis'
b. stretched vertically by a factor of 4, reflected over the x-axis
c. stretched vertically by a factor of 4, reflected over the y-axis
d. shrank vericallyby a factor of 1/4, reflected over the x-axis
what is the vertical shift?
a. 2 units upward
b. 5 units upward
c. 2 units downward
d. 5 units downward
To obtain the graph of y = -1/4(x-2) from the graph of y = |x|, we need to perform several transformations.
First, let's consider the effect of the factor in front of the expression (x-2), which is -1/4. This factor will cause a vertical stretch or shrink of the graph. Since the absolute value function is symmetric around the y-axis, the graph of y = |x| is reflected over the y-axis.
To determine the vertical stretch or shrink, we can compare the absolute value function y = |x| with y = -1/4(x-2). The expression (x-2) in the latter function gives a horizontal shift to the right by 2 units. Additionally, the coefficient -1/4 indicates a vertical shrink by a factor of 1/4 since it is less than 1 in absolute value.
So far, we have determined that the graph of y = -1/4(x-2) is a vertically shrunk and reflected version of the graph of y = |x| over the y-axis.
Now, let's move on to the vertical shift. The vertical shift refers to the movement of the graph up or down. In this case, there is no vertical shift present since there is no addition or subtraction of a constant in the equation y = -1/4(x-2), which means the graph remains unchanged in its vertical position.
To summarize the transformations:
- The graph of y = -1/4(x-2) is obtained from y = |x| by reflecting it over the y-axis.
- It is also vertically shrunk by a factor of 1/4.
- There is no vertical shift.
Therefore, the correct answers to the questions are:
1. The graph is obtained by moving 2 units to the right. So, the answer is b. 2 units to the right.
2. The graph is vertically shrunk by a factor of 1/4 and reflected over the y-axis. So, the answer is a. Shrunk vertically by a factor of 1/4, reflected over the y-axis.
3. There is no vertical shift, so the answer is d. No vertical shift.