Which graph represents y = StartRoot x minus 4 EndRoot?
On a coordinate plane, an absolute value curve opens down and to the right in quadrant 4 and starts at y = negative 4.
On a coordinate plane, an absolute value curve opens down and to the right in quadrant 1 and starts at x = 4.
On a coordinate plane, an absolute value curve opens down and to the right in quadrants 1 and 2 and starts at x = negative 4.
On a coordinate plane, an absolute value curve opens down and to the right in quadrant 1 and starts at y = 4.

The equation \( y = \sqrt{x - 4} \) represents a square root function, which has specific characteristics:

1. The square root function \( \sqrt{x} \) is defined only for \( x \geq 0 \), so \( x - 4 \geq 0 \), meaning the domain of this function is \( x \geq 4 \). This shifts the graph to the right by 4 units.

2. The square root function typically starts at a point and increases slowly as \( x \) increases. In this case, the graph starts at the point \( (4, 0) \), which corresponds to when \( x = 4 \) and \( y = \sqrt{4 - 4} = 0 \).

3. The graph of \( y = \sqrt{x - 4} \) opens upward to the right, not downwards, and it does not involve absolute value. 

Based on these characteristics, the correct graph should open upward and start at \( x = 4 \) in quadrant 1. The second option describes this behavior:

**On a coordinate plane, an absolute value curve opens down and to the right in quadrant 1 and starts at x = 4.**

While it mentions an "absolute value curve" instead of a square root curve, this is likely a misdescription in the problem. The key detail is that it starts at \( x = 4 \) and opens to the right in quadrant 1.

Would you like more details, or do you have any questions? Here are some related questions:

1. What is the domain and range of the function \( y = \sqrt{x - 4} \)?
2. How does shifting the square root function \( y = \sqrt{x} \) affect the graph?
3. How do you determine the starting point of a square root function?
4. Can the square root function ever produce negative y-values?
5. What happens to the graph of \( y = \sqrt{x - a} \) as \( a \) changes?

**Tip:** The graph of a square root function always starts at a point and increases to the right, since square root values are non-negative.

Which graph represents y = StartRoot x minus 4 EndRoot? On a coordinate plane, an absolute value curve opens down and to the right in quadrant 4 and starts at y = negative 4. On a coordinate plane, an absolute value curve opens down and to the right in quadrant 1 and starts at x = 4. On a coordinate plane, an absolute value curve opens down and to the right in quadrants 1 and 2 and starts at x = negative 4. On a coordinate plane, an absolute value curve opens down and to the right in quadrant 1 and starts at y = 4.

Explore the graph of y = √(x - 4), a square root function that shifts 4 units to the right, starting at (4, 0) in quadrant 1. Understand how the domain, range, and transformation affect the graph's appearance. Suitable for Grades 9-10 students learning about function transformations and graphing techniques.

Math Problem Statement

Solution

Ask a new question for Free

By Image

Math Problem Analysis

Mathematical Concepts

Formulas

Theorems

Suitable Grade Level

Related Recommendation