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.
Transcript text: Consider the following function.
\[
t(x)=\frac{1}{x+5}-3
\]
Step 1 of 4: Determine the more basic function that has been shifted, reflected, stretched, or compressed.
Solution
Solution Steps
Step 1: Identify the Original Function
The function given is
t(x)=x+51−3
To determine the more basic function that has been transformed, we start with the original function
f(x)=x1
Step 2: Analyze the Transformations
The function t(x) can be derived from f(x) through a series of transformations:
Horizontal Shift: The term x+5 indicates a horizontal shift to the left by 5 units. Thus, we can express this as:
f(x)→f(x+5)=x+51
Vertical Shift: The subtraction of 3 indicates a vertical shift downward by 3 units. Therefore, we have:
f(x+5)→f(x+5)−3=x+51−3
Step 3: Summary of Transformations
The transformations applied to the original function f(x)=x1 to obtain t(x) are:
A horizontal shift to the left by 5 units.
A vertical shift downward by 3 units.
Final Answer
The more basic function that has been transformed is