Questions: The graph of f(x) shifted left 4 units and shifted down 1 units. f(x) = sqrt(x-4) - 1 f(x) = sqrt(x-4) + 1 f(x) = sqrt(x+4) - 1 f(x) = sqrt(x+4) + 1 The graph of f(x) stretched vertically by a factor of 2 . f(x) = 2 sqrt(x) f(x) = 1/2 sqrt(x) f(x) = sqrt(2 x) f(x) = sqrt(1/2 x)

Solution Steps

To solve the given problems, we need to understand the transformations applied to the function \( f(x) \).

1. For the first part, we need to identify the correct transformation for shifting the graph of \( f(x) \) left by 4 units and down by 1 unit.
2. For the second part, we need to identify the correct transformation for stretching the graph of \( f(x) \) vertically by a factor of 2.

1. Shifting the graph left by 4 units and down by 1 unit:

   • Shifting left by 4 units means replacing \( x \) with \( x + 4 \).
   • Shifting down by 1 unit means subtracting 1 from the function.
   • Therefore, the transformed function is \( f(x) = \sqrt{x + 4} - 1 \).

2. Stretching the graph vertically by a factor of 2:

   • Stretching vertically by a factor of 2 means multiplying the function by 2.
   • Therefore, the transformed function is \( f(x) = 2 \sqrt{x} \).

To shift the graph of \( f(x) \) left by 4 units, we replace \( x \) with \( x + 4 \). To shift it down by 1 unit, we subtract 1 from the function. Thus, the transformed function is given by:

\[ f(x) = \sqrt{x + 4} - 1 \]

To stretch the graph of \( f(x) \) vertically by a factor of 2, we multiply the function by 2. Therefore, the transformed function is:

\[ f(x) = 2 \sqrt{x} \]

Final Answer