Question

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?

Answer 1

Answer:

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

  $y=a(e)^{kx}$ 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 , $e^{k}$

∵ $y=a(e)^{kx}$

∵ x = 0 and y = 4 ⇒ 1st ordered pair

- Substitute x and y in the equation

∴ $4=a(e)^{k(0)}$

∴ $4=a(e)^{0}$

- The value of $e^{0}$ = 1

∴ a = 4

- Substitute the value of a in the equation

∴ $y=4(e)^{kx}$

∵ x = 1 and y = 5 ⇒ 1st ordered pair

- Substitute x and y in the equation

∴ $5=4(e)^{k(1)}$

∴ $5=4(e)^{k}$

- Divide both sides by 4

∴ $e^{k}$ = 1.25

- Substitute the value of $e^{k}$ in the equation

∴ $y=4(1.25)^{x}$

- 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}

Answer 2

Answer:

The Answer is C!

The domain is the set of real numbers, and the range is y > 0.

Step-by-step explanation: