Question
Which function matches the graph?
(1 point)
Responses
g(x)={x + 1, x < 53, x ≥ 3
g(x)={x + 1, x < 53, x ≥ 3
g(x)={−x + 1, x ≤−43, x > −4
g(x)={−x + 1, x ≤−43, x > −4
g(x)={x − 1, x ≤15, x > 3
g(x)={x − 1, x ≤15, x > 3
g(x)={−x, x < −43, x ≥−4
g(x)={−x, x < −43, x ≥−4
(1 point)
Responses
g(x)={x + 1, x < 53, x ≥ 3
g(x)={x + 1, x < 53, x ≥ 3
g(x)={−x + 1, x ≤−43, x > −4
g(x)={−x + 1, x ≤−43, x > −4
g(x)={x − 1, x ≤15, x > 3
g(x)={x − 1, x ≤15, x > 3
g(x)={−x, x < −43, x ≥−4
g(x)={−x, x < −43, x ≥−4
Answers
GPT-4o mini
To determine which function matches the graph, we would need to analyze the characteristics of each option based on the provided piecewise definitions. However, without the actual graph to reference, I can only describe a method for evaluating them.
1. Look for critical points in the piecewise functions where the definition changes (i.e., at the boundaries):
- For \( g(x) = \{ x + 1 \, \text{if} \, x < 5, \, 3 \, \text{if} \, x \geq 3 \} \), the critical point is at \( x = 5 \).
- For \( g(x) = \{ -x + 1 \, \text{if} \, x \leq -4, \, 3 \, \text{if} \, x > -4 \} \), the critical point is at \( x = -4 \).
- For \( g(x) = \{ x - 1 \, \text{if} \, x \leq 15, \, 3 \, \text{if} \, x > 3 \} \), the critical point is at \( x = 3 \).
- For \( g(x) = \{ -x \, \text{if} \, x < -4, \, x \geq -4 \} \), the critical point is also at \( x = -4 \).
2. Evaluate the slopes and intercepts for each piece of the functions to see how they would behave in relation to the graph you have.
3. Identify regions where the function is defined and see if that aligns with the graph.
4. If you have specific points, you can check to see if they fit any of the conditions outlined in the proposed piecewise functions.
You can post the characteristics of the graph, and I can help you confirm which function matches!
1. Look for critical points in the piecewise functions where the definition changes (i.e., at the boundaries):
- For \( g(x) = \{ x + 1 \, \text{if} \, x < 5, \, 3 \, \text{if} \, x \geq 3 \} \), the critical point is at \( x = 5 \).
- For \( g(x) = \{ -x + 1 \, \text{if} \, x \leq -4, \, 3 \, \text{if} \, x > -4 \} \), the critical point is at \( x = -4 \).
- For \( g(x) = \{ x - 1 \, \text{if} \, x \leq 15, \, 3 \, \text{if} \, x > 3 \} \), the critical point is at \( x = 3 \).
- For \( g(x) = \{ -x \, \text{if} \, x < -4, \, x \geq -4 \} \), the critical point is also at \( x = -4 \).
2. Evaluate the slopes and intercepts for each piece of the functions to see how they would behave in relation to the graph you have.
3. Identify regions where the function is defined and see if that aligns with the graph.
4. If you have specific points, you can check to see if they fit any of the conditions outlined in the proposed piecewise functions.
You can post the characteristics of the graph, and I can help you confirm which function matches!