The problem consists of three statements regarding transformations of functions. The task is to identify the transformation that maps $f(x)$ to $g(x)$ in each statement.

1. Problem Description

The problem consists of three statements regarding transformations of functions. The task is to identify the transformation that maps $f(x)$ to $g(x)$ in each statement.

2. Solution Steps

Statement 1: $g(x) = (x + 10)^2$ and $f(x) = x^2$

The transformation is of the form $g(x) = f(x + 10)$. Replacing $x$ with $x+10$ shifts the graph horizontally. Since we have $x+10$, the graph is shifted 10 units to the left.

Statement 2: $g(x) = x^2 + 10$ and $f(x) = x^2$

The transformation is of the form $g(x) = f(x) + 10$. Adding 10 to the function shifts the graph vertically. Since we have $+10$, the graph is shifted 10 units upwards.

Statement 3: $g(x) = 10\sqrt{x}$ and $f(x) = \sqrt{x}$

The transformation is of the form $g(x) = 10f(x)$. Multiplying the function by 10 stretches the graph vertically by a factor of

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3. Final Answer

1. The graph of $g(x) = (x + 10)^2$ can be obtained from shifting the graph of $f(x) = x^2$ to the left 10 units.

2. The graph of $g(x) = x^2 + 10$ can be obtained from shifting the graph of $f(x) = x^2$ upwards 10 units.

3. The graph of $g(x) = 10\sqrt{x}$ can be obtained from stretching the graph of $f(x) = \sqrt{x}$ vertically by a factor 10.