Start by performing a reflection across the x-axis.
The parent graph 3^x is reflected across y-axis, stretched by a factor of 2, and translated 1 unit to the left and 5 units down
Practice makes perfect
We want to determine how the graph of the given function compares to the graph of the parent function, which is an exponential function. In other words, we want to find and perform transformations on the graph of 3^x that result in the graph the given function.
y=- 2(3)^(x+ 1)- 5
Looking at the function, we can see that it has been reflected across the x-axis, stretched by a factor of 2, translated 1 unit to the left, and translated 5 units down. Let's show the transformations one at a time.
Reflection
Let's start by considering the parent function y=3^x. If we perform a reflection across the x-axis, the resulting function is y=- (3)^x.
Stretch
If we multiply - (3)^x by 2, we obtain a vertical stretch by a factor of 2. The resulting function is y=- 2(3)^x.
Horizontal Translation
Now, we need to consider the function y=- 2(3)^(x+1). This is a horizontal translation of y=- 2(3)^x to the left by 1 unit.
Vertical Translation
Finally, we will consider the function y=- 2(3)^(x+1)-5. This is a vertical translation of y=- 2(3)^(x+1) down by 5 units.
Extra
Possible Transformations
The following table illustrates the general form for all possible transformations of functions.
