PROBLEMS ON DOMAIN AND RANGE OF EXPONENTIAL FUNCTIONS

Problem 1 :

What is the domain of the exponential function

f(x) = 14(0.8)x ?

Solution :

f(x) = 14(0.8)x

Domain for exponential function will be all real number, so domain is (-∞, ∞).

Problem 2 :

What is the range of exponential function y = 120 (7x) ?

Solution :

Finding horizontal asymptote for the exponential function, it is easier to fix the range.

The function which is in the form y = abx - h + k

Here y = k is the horizontal asymptote.

Here the horizontal asymptote is y = 0, then range is y > 0

Problem 3 :

The graph of y = (2/3)x is shown below. What is the range of the function y ?

domain-and-range-of-exp-function-q1

Solution :

From the graph, the horizontal asymptote is y = 0. Then the range is y > 0.

Problem 4 :

What is the domain of f(x) = 6(1.8)x?

Solution :

Domain of the function is all real values.

Problem 5 :

The graph of the exponential function y = -400 (5)x is shown below.

domain-and-range-of-exp-function-q2.png

What is the range of the function ?

Solution :

From the graph, there is a reflection across x-axis, it is decreasing function. 

So, the range is y < 0.

Problem 6 :

The table below shows points that belongs to the function.

domain-and-range-of-exp-function-q3.png

Solution :

Exponential function will be in the form y = abx -------(1)

Applying the point (0, 1) in the function, we get

1 = ab0

1 = a(1)

a = 1

By applying the value of a in (1), we get

y = 1(b)x

By applying the point (1, 3), we get

3 = 1(b)1

b = 3

So, the required function is y = 3x .

  • Domain is all real values.
  • Range is y > 0.

Problem 7 :

domain-and-range-of-exp-function-q4.png

Solution :

Domain is x < 2.

Horizontal asymptote is y = -5, so the range is y > -5.

Problem 8 :

domain-and-range-of-exp-function-q5.png

Solution :

Domain is all real values.

Horizontal asymptote is y = -5, so the range is y > -5.

Problem 9 :

The volume V, the air remaining in an inflated balloon can be modeled by the function

V = 1000 (0.85)x

where x represents the number of days that have passed since inflating the balloon. What is the reasonable domain for the situation.

Solution :

V = 1000 (0.85)x

Since it is exponential function, it is defined for every real numbers.

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