Question
is it graph 1, 2, 3, or 4? Which graph accurately demonstrates the relationship between the functions f(x)=x−−√
and f(x)=x−−√+3
?(1 point)
Responses
Two curves are graphed on a coordinate plane. The x-axis ranges from negative 3 to 3 in increments of 1. The y-axis ranges from negative 6 to 6 in increments of 2.
Image with alt text: Two curves are graphed on a coordinate plane. The x-axis ranges from negative 3 to 3 in increments of 1. The y-axis ranges from negative 6 to 6 in increments of 2.
Two curves are graphed on a coordinate plane. The x-axis ranges from negative 3 to 3 in increments of 1. The y-axis ranges from negative 4 to 4 in increments of 2.
Image with alt text: Two curves are graphed on a coordinate plane. The x-axis ranges from negative 3 to 3 in increments of 1. The y-axis ranges from negative 4 to 4 in increments of 2.
Two curves are graphed on a coordinate plane. The x-axis ranges from negative 3 to 3 in increments of 1. The y-axis ranges from negative 6 to 6 in increments of 2.
Image with alt text: Two curves are graphed on a coordinate plane. The x-axis ranges from negative 3 to 3 in increments of 1. The y-axis ranges from negative 6 to 6 in increments of 2.
Two curves are graphed on a coordinate plane. The x-axis ranges from negative 3 to 3 in increments of 1. The y-axis ranges from negative 4 to 4 in increments of 2.
and f(x)=x−−√+3
?(1 point)
Responses
Two curves are graphed on a coordinate plane. The x-axis ranges from negative 3 to 3 in increments of 1. The y-axis ranges from negative 6 to 6 in increments of 2.
Image with alt text: Two curves are graphed on a coordinate plane. The x-axis ranges from negative 3 to 3 in increments of 1. The y-axis ranges from negative 6 to 6 in increments of 2.
Two curves are graphed on a coordinate plane. The x-axis ranges from negative 3 to 3 in increments of 1. The y-axis ranges from negative 4 to 4 in increments of 2.
Image with alt text: Two curves are graphed on a coordinate plane. The x-axis ranges from negative 3 to 3 in increments of 1. The y-axis ranges from negative 4 to 4 in increments of 2.
Two curves are graphed on a coordinate plane. The x-axis ranges from negative 3 to 3 in increments of 1. The y-axis ranges from negative 6 to 6 in increments of 2.
Image with alt text: Two curves are graphed on a coordinate plane. The x-axis ranges from negative 3 to 3 in increments of 1. The y-axis ranges from negative 6 to 6 in increments of 2.
Two curves are graphed on a coordinate plane. The x-axis ranges from negative 3 to 3 in increments of 1. The y-axis ranges from negative 4 to 4 in increments of 2.
Answers
Answered by
GPT-4o mini
To determine which graph accurately demonstrates the relationship between the functions \( f(x) = \sqrt{x} \) and \( f(x) = \sqrt{x} + 3 \), we should consider the properties of these functions:
1. **Function \( f(x) = \sqrt{x} \)**:
- This function has a domain of \( x \geq 0 \) (since square root is only defined for non-negative numbers).
- The range starts at \( 0 \) (when \( x = 0 \)) and increases indefinitely as \( x \) increases.
2. **Function \( f(x) = \sqrt{x} + 3 \)**:
- This function also has a domain of \( x \geq 0 \).
- The range starts at \( 3 \) (when \( x = 0 \)) and increases indefinitely.
From this analysis, we know that:
- The graph of \( f(x) = \sqrt{x} \) will start at the point (0, 0) and will be in the first quadrant, increasing to the right.
- The graph of \( f(x) = \sqrt{x} + 3 \) will start at the point (0, 3) and also increase to the right, but it will be translated upwards by 3 units compared to the first graph.
Now, we look for a graph where:
- One curve begins at the origin (0,0) and the second curve begins at (0,3), maintaining the same shape but shifted upwards.
Now we can evaluate the options you provided:
- Each option mentions images containing two curves, with varying ranges of the y-axis.
- Since the appropriate y-values for \( f(x) = \sqrt{x} \) range from 0 to above, while for \( f(x) = \sqrt{x} + 3 \), it starts from 3 and goes higher.
The graphs that display this correct upward shift to match our analysis would be those where one curve starts at (0,0) and the other starts right above at (0,3).
However, as I do not have access to the graphs themselves, I recommend you choose the option where one curve reaches the y-value of 0 (for \( f(x) = \sqrt{x} \)) and the other curve starts from y=3 (for \( f(x) = \sqrt{x} + 3 \)). If one of the graphs clearly shows this relationship, that would be the correct answer. If you can provide more detail or a better description of the differences in the graphs, I may be able to help you further!
1. **Function \( f(x) = \sqrt{x} \)**:
- This function has a domain of \( x \geq 0 \) (since square root is only defined for non-negative numbers).
- The range starts at \( 0 \) (when \( x = 0 \)) and increases indefinitely as \( x \) increases.
2. **Function \( f(x) = \sqrt{x} + 3 \)**:
- This function also has a domain of \( x \geq 0 \).
- The range starts at \( 3 \) (when \( x = 0 \)) and increases indefinitely.
From this analysis, we know that:
- The graph of \( f(x) = \sqrt{x} \) will start at the point (0, 0) and will be in the first quadrant, increasing to the right.
- The graph of \( f(x) = \sqrt{x} + 3 \) will start at the point (0, 3) and also increase to the right, but it will be translated upwards by 3 units compared to the first graph.
Now, we look for a graph where:
- One curve begins at the origin (0,0) and the second curve begins at (0,3), maintaining the same shape but shifted upwards.
Now we can evaluate the options you provided:
- Each option mentions images containing two curves, with varying ranges of the y-axis.
- Since the appropriate y-values for \( f(x) = \sqrt{x} \) range from 0 to above, while for \( f(x) = \sqrt{x} + 3 \), it starts from 3 and goes higher.
The graphs that display this correct upward shift to match our analysis would be those where one curve starts at (0,0) and the other starts right above at (0,3).
However, as I do not have access to the graphs themselves, I recommend you choose the option where one curve reaches the y-value of 0 (for \( f(x) = \sqrt{x} \)) and the other curve starts from y=3 (for \( f(x) = \sqrt{x} + 3 \)). If one of the graphs clearly shows this relationship, that would be the correct answer. If you can provide more detail or a better description of the differences in the graphs, I may be able to help you further!