Question
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Part 1
How does the graph of f left parenthesis x right parenthesis equals 2 Superscript x plus 2f(x)=2x+2 compare to the graph of g left parenthesis x right parenthesis equals 2 Superscript x Baseline plus 2g(x)=2x+2?
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Part 1
The graph of f(x) is a translation of the parent function h left parenthesis x right parenthesis equals 2 Superscript xh(x)=2x enter your response here unit(s)
▼
to the right,
upwards,
downwards,
to the left,
whereas the graph of g(x) is a translation of the parent function h left parenthesis x right parenthesis equals 2 Superscript xh(x)=2x enter your response here unit(s)
▼
downwards.
upwards.
to the right.
to the left.
(Type whole numbers.)
Part 1
How does the graph of f left parenthesis x right parenthesis equals 2 Superscript x plus 2f(x)=2x+2 compare to the graph of g left parenthesis x right parenthesis equals 2 Superscript x Baseline plus 2g(x)=2x+2?
Question content area bottom
Part 1
The graph of f(x) is a translation of the parent function h left parenthesis x right parenthesis equals 2 Superscript xh(x)=2x enter your response here unit(s)
▼
to the right,
upwards,
downwards,
to the left,
whereas the graph of g(x) is a translation of the parent function h left parenthesis x right parenthesis equals 2 Superscript xh(x)=2x enter your response here unit(s)
▼
downwards.
upwards.
to the right.
to the left.
(Type whole numbers.)
Answers
Answered by
GPT-4o mini
To analyze the functions \( f(x) = 2^x + 2 \) and \( g(x) = 2^x + 2 \), we first note that both functions are actually identical, meaning their graphs will also be identical. Let's break down the transformations to the parent function \( h(x) = 2^x \).
### Comparing the functions:
1. **Function f(x)**:
- The function \( f(x) = 2^x + 2 \) is the parent function \( h(x) = 2^x \) shifted upwards by 2 units.
2. **Function g(x)**:
- Similarly, the function \( g(x) = 2^x + 2 \) is also the parent function \( h(x) = 2^x \) shifted upwards by 2 units.
### Answering the questions regarding translations:
- Since both functions are the same, their behaviors will also be identical.
Here’s how you can fill in the responses:
1. The graph of \( f(x) \) is a translation of the parent function \( h(x) = 2^x \) **2 unit(s)** **upwards**.
2. The graph of \( g(x) \) is a translation of the parent function \( h(x) = 2^x \) **2 unit(s)** **upwards**.
So, the completed response would be:
- The graph of f(x) is a translation of the parent function h(x) = 2^x **2 unit(s)** upward, whereas the graph of g(x) is a translation of the parent function h(x) = 2^x **2 unit(s)** upward.
### Comparing the functions:
1. **Function f(x)**:
- The function \( f(x) = 2^x + 2 \) is the parent function \( h(x) = 2^x \) shifted upwards by 2 units.
2. **Function g(x)**:
- Similarly, the function \( g(x) = 2^x + 2 \) is also the parent function \( h(x) = 2^x \) shifted upwards by 2 units.
### Answering the questions regarding translations:
- Since both functions are the same, their behaviors will also be identical.
Here’s how you can fill in the responses:
1. The graph of \( f(x) \) is a translation of the parent function \( h(x) = 2^x \) **2 unit(s)** **upwards**.
2. The graph of \( g(x) \) is a translation of the parent function \( h(x) = 2^x \) **2 unit(s)** **upwards**.
So, the completed response would be:
- The graph of f(x) is a translation of the parent function h(x) = 2^x **2 unit(s)** upward, whereas the graph of g(x) is a translation of the parent function h(x) = 2^x **2 unit(s)** upward.