# DOMAIN AND RANGE OF EXPONENTIAL FUNCTIONS PRACTICE

Every exponential function will be in the form y = abx

How to find domain of exponential function ?

Domain is set of all possible inputs. For a exponential function all real numbers are possible inputs. So, domain of the exponential function will be (-∞, ∞).

How to find the range of exponential function ?

It is simple to find the range of the exponential function after fixing the horizontal asymptote.

y = abx - h + k

Here y = k is the horizontal asymptote.

Graph each function. Label two points.

Problem 1 :

f(x) = 2x + 2

Domain:     Range:

Parent function and transformation:

Solution:

f(x) = 2x + 2

Domain:

Domain is the defined value of x. For this function, the domain is all real numbers.

Range:

Equation of horizontal asymptote is y = 2.

The range is y > 2.

Parent function:

y = a(b)x

f(x) = 2x

Transformation:

Horizontal shift: No shift

Vertical shift: 2 units up

Problem 2 :

f(x) = 3x-1

Domain:     Range:

Parent function and transformation:

Solution:

f(x) = 3x-1

Domain:

Domain is the defined value of x. For this function, the domain is all real numbers.

Range:

The range is y > 0.

Parent function:

y = a(b)x

f(x) = 3x

Transformation:

Horizontal shift: Right 1 unit

Vertical shift: No shift

Problem 3 :

f(x) = 2x-2 - 1

Domain:     Range:

Parent function and transformation:

Solution:

f(x) = 2x-2 - 1

Domain:

Domain is the defined value of x. For this function, the domain is all real numbers.

Range:

Equation of horizontal asymptote is y = -1, since it is exponential growth function, the range is y > -1.

Parent function:

y = a(b)x

f(x) = 2x

Transformation:

Horizontal shift: Right 2 units

Vertical shift: Down 1 unit

Problem 4 :

f(x) = -2x+1 - 3

Domain:     Range:

Parent function and transformation:

Solution:

f(x) = -2x+1 - 3

Domain:

Domain is the defined value of x. For this function, the domain is all real numbers.

Range:

Equation of horizontal asymptote is y = -3, since it is exponential growth function but there is reflection across x-axis and the range is y < -3.

Parent function:

y = a(b)x

f(x) = 2x

Transformation:

Horizontal shift: left 1 unit

Vertical shift: down 3 units

Problem 5 :

f(x) = -(3x+1) + 2

Domain:     Range:

Parent function and transformation:

Solution:

f(x) = -(3x+1) + 2

Domain:

Domain is the defined value of x. For this function, the domain is all real numbers.

Range:

There is a reflection across x-axis, moving horizontally 1 unit to the left and moving up 2 units.

The range is y < 2.

Parent function:

y = a(b)x

f(x) = 3x

Transformation:

Horizontal shift: left 1 unit

Vertical shift: up 2 units

Problem 6 :

Domain:     Range:

Parent function and transformation:

Solution:

Domain:

Domain is the defined value of x. For this function, the domain is all real numbers.

Range:

The range is y > -3.

Parent function:

y = a(b)x

f(x) = 1/2x

Transformation:

Horizontal shift: No shift

Vertical shift: Down 3 units

Problem 7 :

Domain:     Range:

Parent function and transformation:

Solution:

Domain:

Domain is the defined value of x. For this function, the domain is all real numbers.

Range:

The range is y > 1.

Parent function:

y = a(b)x

f(x) = 1/2x

Transformation:

Horizontal shift: No shift

Vertical shift: Up 1 unit

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