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(f)x=x²+5x-1 is shifted 3 units left. The result is g(x). What is g(x)?

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Final Answer:

The function g(x) resulting from shifting f(x) = x^2 + 5x - 1 three units to the left is g(x) = x^2 + 5x - 10.

Step-by-step explanation:

The general form of a quadratic function is f(x) = ax^2 + bx + c, where a, b, and c are constants.

To shift the function f(x) three units to the left, subtract 3 from the variable, resulting in g(x) = (x + 3)^2 + 5(x + 3) - 1.

Expand and simplify g(x) to obtain the shifted quadratic function.

g(x) = (x^2 + 6x + 9) + 5x + 15 - 1.

Combine like terms to get g(x) = x^2 + 5x - 10.

Therefore, g(x) = x^2 + 5x - 10 is the function resulting from shifting f(x) three units to the left.

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