Pregunta
Determine the domain and range of the original function. Express your answer in interval notation.
Ask by Turnbull Morrison. in the United States
Nov 26,2024
Solución de inteligencia artificial de Upstudy
Respuesta verificada por el tutor
Responder
Domain:
Range:
Range:
Solución
Analyze the range of the function
Function by following steps:
Function by following steps:
- step0: Find the range:
- step1: Evaluate:
The domain of the functionis all real numbers greater than or equal to 3, which can be expressed as in interval notation.
The range of the function is
, which means the range is
in interval notation.
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Como
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The Deep Dive
To determine the domain of the function
, we first need to consider the square root. The expression under the square root,
, must be non-negative. Therefore:
So, the domain of
is
.
Now, let’s find the range. Since the square root function outputs values starting from zero and going to infinity, we find:
When we apply the transformation
, it flips the output over the x-axis and scales it, resulting in values starting from 0 going downwards:
- When
, . - As
increases indefinitely, approaches .
Hence, the range of
is
.
In summary:
- Domain:
- Range:

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