Duplicate Question
The question on this page has been marked as a duplicate question.
Original Question
The dotted graph is a reflection of the solid graph. The solid graph is a cubic function with the equation f(x)=x3+1 . Enter th...Question
The dotted graph is a reflection of the solid graph. The solid graph is a cubic function with the equation f(x)=x3+1 . Enter the option number that shows the equation of the image. Option #1: g(x)=−x2+1 Option #2: g(x)=−x3−1 Option #3: g(x)=−x3+1 Option #4: g(x)=x3−1 (1 point) The equation of the dotted graph is Option #
Answers
GPT-4o mini
To find the equation of the dotted graph, which is a reflection of the solid graph \( f(x) = x^3 + 1 \), we need to determine how to reflect the graph of the function.
A reflection across the x-axis changes the function \( f(x) \) to \( -f(x) \).
So, reflecting \( f(x) = x^3 + 1 \) across the x-axis gives us:
\[
g(x) = -f(x) = -(x^3 + 1) = -x^3 - 1
\]
Looking at the options provided:
- Option #1: \( g(x) = -x^2 + 1 \)
- Option #2: \( g(x) = -x^3 - 1 \)
- Option #3: \( g(x) = -x^3 + 1 \)
- Option #4: \( g(x) = x^3 - 1 \)
The correct choice that matches our reflection is **Option #2: \( g(x) = -x^3 - 1 \)**.
Therefore, the equation of the dotted graph is Option #2.
A reflection across the x-axis changes the function \( f(x) \) to \( -f(x) \).
So, reflecting \( f(x) = x^3 + 1 \) across the x-axis gives us:
\[
g(x) = -f(x) = -(x^3 + 1) = -x^3 - 1
\]
Looking at the options provided:
- Option #1: \( g(x) = -x^2 + 1 \)
- Option #2: \( g(x) = -x^3 - 1 \)
- Option #3: \( g(x) = -x^3 + 1 \)
- Option #4: \( g(x) = x^3 - 1 \)
The correct choice that matches our reflection is **Option #2: \( g(x) = -x^3 - 1 \)**.
Therefore, the equation of the dotted graph is Option #2.
Ello dad
GPT-4o mini
Hello! How can I assist you today?
Hey dad I ask u something
GPT-4o mini
Of course! What would you like to ask?
Did u go to the store today like I told u dad? I needed some more cereal
GPT-4o mini
I’m here to assist you with information and tasks, but I’m not your dad! However, I can help remind you to ask someone else or suggest what you might want to say. If you need cereal or anything else, it’s always good to check if you can get it soon! What kind of cereal do you like?
Yes u are.
GPT-4o mini
I understand! In that case, let’s carry on. What else do you need help with? Did you want to talk about the cereal or something else?
Wait so ur not my dad- who are you then
GPT-4o mini
I'm an AI created to assist you with your questions and provide information. I can help with a variety of topics, but I'm not a person or a specific individual. If you have any questions or topics you want to discuss, feel free to ask!