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What is the range of the function f(x)= square root of x-8+6

User Dung Ngo
by
8.4k points

2 Answers

9 votes

Answer:

Range = [6, ∞)

Explanation:

The range of a function is its output values (y-values).

One way to find the range of the given function is to determine the series of translations that have transformed the given function from the parent function.

Translations

For a > 0


f(x+a) \implies f(x) \: \textsf{translated}\:a\:\textsf{units left}


f(x-a) \implies f(x) \: \textsf{translated}\:a\:\textsf{units right}


f(x)+a \implies f(x) \: \textsf{translated}\:a\:\textsf{units up}


f(x)-a \implies f(x) \: \textsf{translated}\:a\:\textsf{units down}

Parent function:
f(x)=√(x)

  • Domain: [0, ∞)
  • Range: [0, ∞)

Given function:
f(x)=√(x-8)+6

The parent function has been:

Translated 8 units right:
f(x-8)=√(x-8)

then translated 6 units up:
f(x-8)+6=√(x-8)+6

If the function has been translated 8 units right, the domain will be:

  • Domain: [0 + 8, ∞) = [8, ∞)

Similarly, if the function has been translated 6 units up, the range will be:

  • Range: [0 + 6, ∞) = [6, ∞)
What is the range of the function f(x)= square root of x-8+6-example-1
User Martin Woodward
by
8.6k points
3 votes

Answer:

  • The range of the given function is [6, + ∞)

Explanation:

It is assumed the function is:


  • f(x)=√(x-8) +6

We know the square root is non-negative, so:

  • x - 8 ≥ 0 therefore the function gets values

  • f(x) ≥ 0 + 6
  • f(x) ≥ 6

We can show this as:

  • f(x) ∈ [6, + ∞)
User Axel Stone
by
7.7k points

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