Several ordered pairs from a continuous exponential function are shown in the table.
a 2-column table has 4 rows. the first column is labeled x with entries 0, 1, 2, 3. the second column is labeled y with entries 4, 5, 6.25, 7.8125.
what are the domain and range of the function?

The domain is {x : x ∈ R} , the range is {y : y > 0}

Step-by-step explanation:

* Lets explain how to solve the problem

- The general form of the continuous exponential function is

  where a is the initial value and k is the growth factor

- We have some ordered pairs from the continuous exponential

  function

- The ordered pairs are:

  (0 , 4) , (1 , 5) , (2 , 6.25) , (3 , 7.8125)

- Lets substitute the values of x and y in the equation to find a ,

∵

∵ x = 0 and y = 4 ⇒ 1st ordered pair

- Substitute x and y in the equation

∴

∴

- The value of = 1

∴ a = 4

- Substitute the value of a in the equation

∴

∵ x = 1 and y = 5 ⇒ 1st ordered pair

- Substitute x and y in the equation

∴

∴

- Divide both sides by 4

∴ = 1.25

- Substitute the value of in the equation

∴

- The domain of the function is all the values of x which make the

  function defines

- The range is the values of y corresponding to x

∵ There is no value of x makes the function undefined

∴ The domain is all real numbers

∵ y never takes a negative value

∴ The range is all the real positive numbers

* The domain is {x : x ∈ R} , the range is {y : y > 0}