Question

The graphs of f(x) = (2/3)^x and g(x) = (2/3)^x-2 are shown below.


Which translation transformed the parent function, f(x), to g(x)?

a translation right 2 units
a translation left 2 units
a translation up 2 units
a translation down 2 units

Answer 1

A translation right 2 units.
The normal f(x) went 2 units to the right, as seen by the graph.
Also, since parent function was (2/3)^x, and transformed into (2/3)^x-2, you should know that all operations performed to the top or x in that particular function means horizontal changes, move right or left, and they're also opposites.
Here, x-2 means move to the right although you'd think it would mean subtracting and moving to the left.

Answer 2

Answer:

Option A is correct

A translation right 2 units

Step-by-step explanation:

Horizontal shift:

To translate the function $y=f(x)$ horizontal, the new graph become

y = f(x+k)

When k > 0 , then the graph shifts left k units

When k < 0 , then the graph shifts right k units

Given the parent fucntion:

$f(x) =(\frac{2}{3})^x$

then, we have the graph

$g(x) =(\frac{2}{3})^{x-2}$

By definition of horizontal shift:

k = -2 < 0

Therefore, a translation right 2 units transformed the parent function, f(x), to g(x)