Algebra and Trigonometry (6th Edition)
6th Edition
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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there’s a 4th answer if none of them are right!

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 .
We have to sketch the graph of the function.
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