To graph the function \( f(x) = (x + 1)^2 \) and its horizontal reflection, we first note that the horizontal reflection of a function \( f(x) \) is represented as \( f(-x) \).
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Finding \( f(-x) \): \[ f(-x) = (-x + 1)^2 = (1 - x)^2 \]
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Now, let's analyze the original function \( f(x) \): The function \( f(x) = (x + 1)^2 \) is a parabola that opens upwards with its vertex at \( (-1, 0) \).
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Next, let’s examine the reflected function \( f(-x) = (1 - x)^2 \): This function is also a parabola that opens upwards, but its vertex is at \( (1, 0) \).
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Now we need to find the reflected point of \( (-4, 9) \): To reflect the point \( (-4, 9) \) over the y-axis (which is what \( f(-x) \) does), we change the sign of the x-coordinate. Therefore, the reflection of the point \( (-4, 9) \) will be at \( (4, 9) \).
The final answer is: The point \( (-4, 9) \) reflects to \( (4, 9) \) in \( f(-x) \).