3x+2 3. Let f(x)%= X-1 a) Identify the undefined value(s). Describe the behavior near each undefined value. b) Identify all zeros of the functions
Unitary Method
The word “unitary” comes from the word “unit”, which means a single and complete entity. In this method, we find the value of a unit product from the given number of products, and then we solve for the other number of products.
Speed, Time, and Distance
Imagine you and 3 of your friends are planning to go to the playground at 6 in the evening. Your house is one mile away from the playground and one of your friends named Jim must start at 5 pm to reach the playground by walk. The other two friends are 3 miles away.
Profit and Loss
The amount earned or lost on the sale of one or more items is referred to as the profit or loss on that item.
Units and Measurements
Measurements and comparisons are the foundation of science and engineering. We, therefore, need rules that tell us how things are measured and compared. For these measurements and comparisons, we perform certain experiments, and we will need the experiments to set up the devices.
![### End Behavior and Graphing Rational Functions
#### End Behavior of Functions
**Question:**
**c) Fill in the following to describe the end behavior of the function**
\[ \text{as } x \to +\infty, \ y \to \underline{\hspace{2cm}} \]
\[ \text{and as } x \to -\infty, \ y \to \underline{\hspace{2cm}} \]
**Graphing Rational Functions**
**Question:**
**d) Then use the information above to help in sketching a graph of**
\[ f(x) = \frac{3x + 2}{x - 1} \]
**Instructions:**
1. Label all zeros.
2. Label all vertical asymptotes.
3. Describe the end behavior.
#### Explanation:
**Graph of the Function \( f(x) = \frac{3x + 2}{x - 1} \)**
1. **Labels of Zeros:**
- **Zeros:** Found by setting the numerator equal to zero and solving for \( x \).
\[ 3x + 2 = 0 \]
\[ x = -\frac{2}{3} \]
2. **Vertical Asymptotes:**
- **Vertical Asymptotes:** Found by setting the denominator equal to zero and solving for \( x \).
\[ x - 1 = 0 \]
\[ x = 1 \]
3. **End Behavior:**
- As \( x \to +\infty \), \( y \) approaches the horizontal asymptote.
- As \( x \to -\infty \), \( y \) approaches the same horizontal asymptote.
- Since the degrees of the numerator and denominator are the same, the horizontal asymptote is found by dividing the leading coefficients.
\[ \frac{3}{1} = 3 \]
- Therefore,
\[ \text{as } x \to +\infty, \ y \to 3 \]
\[ \text{and as } x \to -\infty, \ y \to 3 \]
These steps detail how to analyze and sketch the graph of the given rational function.](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2Fb7c14283-9a82-48f7-90b1-831241c404f8%2Fafe897d5-7aa1-4af0-bc14-f60986ef2ac5%2Fsh6u2np_processed.jpeg&w=3840&q=75)
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