the graph of y= -1/4/x-2 (1/4 over x-2) can be obtained from the graph of y=|x| by which transformations
a. what is the horizontal shift?
a. five units to right
b. 2 units to right
c. 5 units to left
d. 2 units to left
b. by what factor is the graphstretched or shrunk vertically & how is it reflected
a. shrunk vertically by 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, reflectedd over the y-axis
d. shrank vertically by a factor of 1/4, reflectedover the x-axis
c. what is the vertical shift
a. 2 units upward
b. 5 units upward
c. 2 units downward
d. 5 units downward
a.
To determine the transformations that occurred to obtain the graph of y = -1/4 / (x-2) from the graph of y = |x|, we need to analyze the given equation.
a. The horizontal shift can be determined by observing the expression (x-2). In the original graph y = |x|, the "x" term is not shifted or modified. However, in y = -1/4 / (x-2), we have a shift of 2 units to the right. Therefore, the correct answer is b. 2 units to the right.
b. The factor by which the graph is stretched or shrunk vertically can be found by examining the coefficient in front of the function. In the original graph y = |x|, there is no coefficient, indicating no vertical stretch or shrink. However, in y = -1/4 / (x-2), we have a vertical shrink by a factor of 1/4. Additionally, since there is a negative sign outside the fraction, the graph is reflected over the x-axis. Therefore, the correct answer is d. Shrank vertically by a factor of 1/4 and reflected over the x-axis.
c. The vertical shift can be determined by observing the constant term outside the function. In the original graph y = |x|, there is no constant term, indicating no vertical shift. However, in y = -1/4 / (x-2), we have a vertical shift of 2 units downward. Therefore, the correct answer is c. 2 units downward.