h units right if h is positive
|h| units left if h is negative
k - Vertical Translation
k units up if k is positive
|k| units down if k is negative
a - Orientation and Shape
If a<0, the graph is reflected across the x-axis
If |a|>1, the graph is stretched vertically
If 0<|a|<1, the graph is compressed vertically
We need to identify the values of a, h, and k for the given function.
f(x)=(1/3)^(x+2)+1 ⇕
f(x)= 1 (1/3)^(x-( - 2))+ 1
We see above that a= 1, h= - 2, and k= 1. Using the table of transformations, we can determine if the parent graph is translated vertically or horizontally.
h= - 2, the parent function is translated two units to the left.
k= 1, the parent function is translated one unit up.
The student thinks that subtracting a negative or a positive number from the exponent shifts the parent graph vertically and that adding a negative or a positive number to parent function shifts the graph horizontally. However, it should be the other way around.
