Math  /  Algebra

QuestionLet f(x)=2xf(x)=2 \sqrt{x} If g(x)g(x) is the graph of f(x)f(x) shifted up 1 units and right 5 units, write a formula for g(x)g(x). g(x)=g(x)=

Studdy Solution

STEP 1

1. f(x)=2x f(x) = 2 \sqrt{x} is the given function.
2. The graph of f(x) f(x) is to be shifted up 1 unit and right 5 units.
3. Shifting a graph up by 1 unit adds 1 to the function value.
4. Shifting a graph right by 5 units changes x x to x5 x-5 .

STEP 2

1. Apply the horizontal shift (right 5 units) to f(x) f(x) .
2. Apply the vertical shift (up 1 unit) to the horizontally shifted function.
3. Combine the transformations to get the final formula for g(x) g(x) .

STEP 3

Apply the horizontal shift of right 5 units to the function f(x) f(x) . This changes f(x) f(x) to f(x5) f(x-5) .
f(x5)=2x5 f(x-5) = 2 \sqrt{x-5}

STEP 4

Apply the vertical shift of up 1 unit to the function f(x5) f(x-5) . This adds 1 to f(x5) f(x-5) .
g(x)=f(x5)+1=2x5+1 g(x) = f(x-5) + 1 = 2 \sqrt{x-5} + 1

STEP 5

Combine the transformations to get the final formula for g(x) g(x) .
g(x)=2x5+1 g(x) = 2 \sqrt{x-5} + 1
Solution: The formula for g(x) g(x) is:
g(x)=2x5+1 g(x) = 2 \sqrt{x-5} + 1

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