6.1 hw (ha2) (lms graded) describe how the graph of $g(x)=6\\cdot2^{x+1…
The graph of $g(x)$ is shifted 4 units down and 1 unit(s) to the left of $f(x)$.
Question
6.1 hw (ha2) (lms graded)
describe how the graph of $g(x)=6\\cdot2^{x+1}-4$ compares to the graph of $f(x)=6\\cdot2^{x}$.
the graph of $g(x)$ is shifted □ unit(s) □, and □ unit(s) to the □ of $f(x)$.
Solution Steps
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Understand the question
6.1 hw (ha2) (lms graded)
describe how the graph of $g(x)=6\\cdot2^{x+1}-4$ compares to the graph of $f(x)=6\\cdot2^{x}$.
the graph of $g(x)$ is shifted □ unit(s) □, and □ unit(s) to the □ of $f(x)$. -
Explanation
Step1: Identify horizontal shift
For exponential functions, $f(x-h)$ shifts $f(x)$ right $h$ units. Rewrite $g(x)$: $g(x)=6\cdot2^{(x-(-1))}-4$, so $h=-1$. Shift left 1 unit.
Step2: Identify vertical shift
For functions, $f(x)-k$ shifts $f(x)$ down $k$ units. Here, $g(x)=f(x+1)-4$, so shift down 4 units.
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Final answer
The graph of $g(x)$ is shifted 4 units down and 1 unit(s) to the left of $f(x)$.
Answer
Explanation
Step1: Identify horizontal shift
For exponential functions, $f(x-h)$ shifts $f(x)$ right $h$ units. Rewrite $g(x)$: $g(x)=6\cdot2^{(x-(-1))}-4$, so $h=-1$. Shift left 1 unit.
Step2: Identify vertical shift
For functions, $f(x)-k$ shifts $f(x)$ down $k$ units. Here, $g(x)=f(x+1)-4$, so shift down 4 units.
Answer
The graph of $g(x)$ is shifted 4 units down and 1 unit(s) to the left of $f(x)$.
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Subject
mathematics
Sub Subject
calculus
Education Level
high school
Difficulty
unspecified
Question Type
text only
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No
Question Count
1
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completed
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2026-02-09T20:25:52
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6.1 hw (ha2) (lms graded)
describe how the graph of $g(x)=6\\cdot2^{x+1}-4$ compares to the graph of $f(x)=6\\cdot2^{x}$.
the graph of $g(x)$ is shifted □ unit(s) □, and □ unit(s) to the □ of $f(x)$.
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