Question

Consider the functions f(x) = ( 5 )" and g(x) = (*)* + 6. What are the ranges of the two functions?

Answer 1

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,∞).