Question
In the following square root function:
What are the coordinates of the point farthest to the left?
x = ____________
y = ____________
Graph the square root function →
What are the coordinates of the point farthest to the left?
x = ____________
y = ____________
Graph the square root function →
Answers
Answered by
GPT-4o mini
To determine the coordinates of the point farthest to the left for a square root function, we first need to know the standard form of a square root function. The general form is:
\[ y = a\sqrt{x - h} + k \]
where \( (h, k) \) is the vertex of the function, and \( a \) determines whether the graph opens upward or downward, but since we only consider square root functions that open to the right, \( a \) is typically positive.
The domain of the square root function is restricted to values where the expression inside the square root is non-negative. In this case, for the basic square root function \( y = \sqrt{x} \), the smallest value for \( x \) is 0, and thus the point farthest to the left will occur at:
\[ x = 0 \]
When \( x = 0 \), we have:
\[ y = \sqrt{0} = 0 \]
So the coordinates of the point farthest to the left are:
- \( x = 0 \)
- \( y = 0 \)
Thus, the coordinates are:
- **x = 0**
- **y = 0**
If you would like to see a graph of the basic square root function \( y = \sqrt{x} \), it starts at the point (0, 0) and increases from there, opening to the right.
If you have a specific version of the square root function you'd like graphed or analyzed, please provide that equation, and I can give a more detailed answer regarding the coordinates and graphing.
\[ y = a\sqrt{x - h} + k \]
where \( (h, k) \) is the vertex of the function, and \( a \) determines whether the graph opens upward or downward, but since we only consider square root functions that open to the right, \( a \) is typically positive.
The domain of the square root function is restricted to values where the expression inside the square root is non-negative. In this case, for the basic square root function \( y = \sqrt{x} \), the smallest value for \( x \) is 0, and thus the point farthest to the left will occur at:
\[ x = 0 \]
When \( x = 0 \), we have:
\[ y = \sqrt{0} = 0 \]
So the coordinates of the point farthest to the left are:
- \( x = 0 \)
- \( y = 0 \)
Thus, the coordinates are:
- **x = 0**
- **y = 0**
If you would like to see a graph of the basic square root function \( y = \sqrt{x} \), it starts at the point (0, 0) and increases from there, opening to the right.
If you have a specific version of the square root function you'd like graphed or analyzed, please provide that equation, and I can give a more detailed answer regarding the coordinates and graphing.