Question
A function f is given and the indicted transformation are applied to its graph write the equation for the final transformed graph
F(x)=3 under root x shift 7 units to the right
Then y=?
F(x)=3 under root x shift 7 units to the right
Then y=?
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GPT 3.5
To find the equation for the final transformed graph, we need to apply each transformation step by step.
The function f(x) = √(x) represents the square root function.
1. Shift 7 units to the right:
The function g(x) = f(x - 7) represents a shift of 7 units to the right. To perform this transformation, we substitute (x - 7) for x in the function f(x), which gives us g(x) = √(x - 7).
2. Multiply by 3:
The function h(x) = 3g(x) represents a vertical stretch by a factor of 3. To perform this transformation, we multiply the function g(x) by 3, which gives us h(x) = 3√(x - 7).
Therefore, the equation for the final transformed graph is y = 3√(x - 7).
The function f(x) = √(x) represents the square root function.
1. Shift 7 units to the right:
The function g(x) = f(x - 7) represents a shift of 7 units to the right. To perform this transformation, we substitute (x - 7) for x in the function f(x), which gives us g(x) = √(x - 7).
2. Multiply by 3:
The function h(x) = 3g(x) represents a vertical stretch by a factor of 3. To perform this transformation, we multiply the function g(x) by 3, which gives us h(x) = 3√(x - 7).
Therefore, the equation for the final transformed graph is y = 3√(x - 7).
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