Answer:
a) horizontal compression with a factor of 0.5 and a horizontal reflection over the y-axis.
b) Pick one the two correct answers:
translation of 2 units right
translation of 2 units down
Step-by-step explanation:
If function f(x) is transformed into f(ax) then it is stretched or compressed horizontally.
If |a| > 1 it is compressed horizontally.
If 0 < |a| < 1, it is stretched horizontally.
If a is negative, then it is reflected over the y-axis.
a) Compare y = -2x with y = x.
The change is in that x became -2x.
Here, a = -2.
Since |-2| = 2, and 2 > 1, it has a compression of a factor of 2 horizontally.
Also, since -2 is a negative number, it is reflected over the y-axis.
Answer: horizontal compression with a factor of 0.5 and a horizontal reflection over the y-axis.
If function f(x) is transformed into f(x) + b then it is translated vertically b units. If b > 0, the translation is b units up. If b < 0, the translation is b units down.
b) y = x - 2
This can be thought of the function f(x) becoming f(x) - 2.
It is a translation of 2 units down.
Interestingly, in this case, this can also be thought of x being replaced by x - 2 which is a translation of 2 units to the right.
Answer:
There are two correct answers (use only one of the two below):
translation of 2 units right
translation of 2 units down
