1. Which graph represents f(x)=√2-1?

Algebra and Trigonometry (6th Edition)
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ISBN:9780134463216
Author:Robert F. Blitzer
Publisher:Robert F. Blitzer
ChapterP: Prerequisites: Fundamental Concepts Of Algebra
Section: Chapter Questions
Problem 1MCCP: In Exercises 1-25, simplify the given expression or perform the indicated operation (and simplify,...
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**Question:** Which graph represents the function \( f(x) = \frac{1}{2} \sqrt{2x - 1} \)?

**Graph Descriptions:**

1. **First Graph:** 
   - The curve starts from the left, slightly above the x-axis, and rises smoothly, showing an increasing trend.
   - It exhibits a gradual upward slope, and the function becomes steeper as it moves to the right.
   - This is characteristic of a square root function, shifted to the right.

2. **Second Graph:**
   - This graph starts at the origin or slightly to the right, with a curve that increases steadily but not steeply.
   - The function appears to have a similar rise as the first but is less steep overall.

3. **Third Graph:**
   - This curve starts high on the y-axis and slopes downward as it moves to the right.
   - The graph trends downward, indicating a decreasing function, which is not typical of a square root function starting at a positive point on the x-axis.

**Analysis:**
To determine which graph represents the function \( f(x) = \frac{1}{2} \sqrt{2x - 1} \), consider the following characteristics:
- The function is a transformed square root function.
- It includes a horizontal shift to the right due to the term \(2x - 1\).
- It starts at \(x = 0.5\) (since the expression under the square root must be non-negative, \(2x - 1 \geq 0 \)).
- The slope gradually becomes steeper with increasing x-values.

Given these properties, the **first graph** most closely represents the function \( f(x) = \frac{1}{2} \sqrt{2x - 1} \). This graph exhibits the typical shape of a square root function with a rightward shift and an upward trend starting above \(x = 0.5\).
Transcribed Image Text:**Question:** Which graph represents the function \( f(x) = \frac{1}{2} \sqrt{2x - 1} \)? **Graph Descriptions:** 1. **First Graph:** - The curve starts from the left, slightly above the x-axis, and rises smoothly, showing an increasing trend. - It exhibits a gradual upward slope, and the function becomes steeper as it moves to the right. - This is characteristic of a square root function, shifted to the right. 2. **Second Graph:** - This graph starts at the origin or slightly to the right, with a curve that increases steadily but not steeply. - The function appears to have a similar rise as the first but is less steep overall. 3. **Third Graph:** - This curve starts high on the y-axis and slopes downward as it moves to the right. - The graph trends downward, indicating a decreasing function, which is not typical of a square root function starting at a positive point on the x-axis. **Analysis:** To determine which graph represents the function \( f(x) = \frac{1}{2} \sqrt{2x - 1} \), consider the following characteristics: - The function is a transformed square root function. - It includes a horizontal shift to the right due to the term \(2x - 1\). - It starts at \(x = 0.5\) (since the expression under the square root must be non-negative, \(2x - 1 \geq 0 \)). - The slope gradually becomes steeper with increasing x-values. Given these properties, the **first graph** most closely represents the function \( f(x) = \frac{1}{2} \sqrt{2x - 1} \). This graph exhibits the typical shape of a square root function with a rightward shift and an upward trend starting above \(x = 0.5\).
Expert Solution
Step 1

The given function fx=122x-1.

We have to sketch the graph of the function.

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