Answer:
The range of the function is the set of all possible values that function can take. Both given functions
y=\left(\dfrac{4}{5}\right)^xy=(
5
4
)
x
and y=\left(\dfrac{4}{5}\right)^x+6y=(
5
4
)
x
+6
are exponential functions with base \dfrac{4}{5}.
5
4
.
The graphs of these function you can see in attached diagram.
The range of the function y=\left(\dfrac{4}{5}\right)^xy=(
5
4
)
x
is (0,\infty).(0,∞).
The range of the function y=\left(\dfrac{4}{5}\right)^x+6y=(
5
4
)
x
+6 (this function is translated function y=\left(\dfrac{4}{5}\right)^xy=(
5
4
)
x
6 units up) is (6,\infty).(6,∞).
