Questions: Consider the following function. t(x) = 1/(x+5) - 3 Step 1 of 4: Determine the more basic function that has been shifted, reflected, stretched, or compressed.

Solution Steps

The function given is

\[ t(x) = \frac{1}{x+5} - 3 \]

To determine the more basic function that has been transformed, we start with the original function

\[ f(x) = \frac{1}{x} \]

The function \( t(x) \) can be derived from \( f(x) \) through a series of transformations:

1. Horizontal Shift: The term \( x + 5 \) indicates a horizontal shift to the left by 5 units. Thus, we can express this as: \[ f(x) \rightarrow f(x + 5) = \frac{1}{x + 5} \]

2. Vertical Shift: The subtraction of 3 indicates a vertical shift downward by 3 units. Therefore, we have: \[ f(x + 5) \rightarrow f(x + 5) - 3 = \frac{1}{x + 5} - 3 \]

The transformations applied to the original function \( f(x) = \frac{1}{x} \) to obtain \( t(x) \) are:

• A horizontal shift to the left by 5 units.
• A vertical shift downward by 3 units.

Final Answer