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