Question
Translate the equation 2 units to the down. Vertically compress by a factor of 1/2
Y=4(x-4)^(x+7)-6then arrow sign
Y=4(x-4)^(x+7)-6then arrow sign
Answers
GPT-4o mini
To translate the equation 2 units down and compress it vertically by a factor of 1/2, we can break it down into two transformations:
1. **Translate down by 2 units:** This involves subtracting 2 from the entire function.
2. **Vertically compress by a factor of 1/2:** To achieve this, we multiply the entire function by 1/2.
Starting with the original equation:
\[ Y = 4(x - 4)^{(x + 7)} - 6 \]
1. **Translate down by 2 units:**
\[ Y = 4(x - 4)^{(x + 7)} - 6 - 2 \]
\[ Y = 4(x - 4)^{(x + 7)} - 8 \]
2. **Vertically compress by a factor of 1/2:**
\[ Y = \frac{1}{2} \left(4(x - 4)^{(x + 7)} - 8\right) \]
This simplifies as follows:
\[ Y = 2(x - 4)^{(x + 7)} - 4 \]
Putting it all together, the equation after the transformations is:
\[ Y = 2(x - 4)^{(x + 7)} - 4 \]
Thus, the final answer after the transformations is:
\[ Y = 2(x - 4)^{(x + 7)} - 4 \]
So we can express it with the arrow notation:
\[ Y = 4(x-4)^{(x+7)} - 6 \rightarrow Y = 2(x - 4)^{(x + 7)} - 4 \]
1. **Translate down by 2 units:** This involves subtracting 2 from the entire function.
2. **Vertically compress by a factor of 1/2:** To achieve this, we multiply the entire function by 1/2.
Starting with the original equation:
\[ Y = 4(x - 4)^{(x + 7)} - 6 \]
1. **Translate down by 2 units:**
\[ Y = 4(x - 4)^{(x + 7)} - 6 - 2 \]
\[ Y = 4(x - 4)^{(x + 7)} - 8 \]
2. **Vertically compress by a factor of 1/2:**
\[ Y = \frac{1}{2} \left(4(x - 4)^{(x + 7)} - 8\right) \]
This simplifies as follows:
\[ Y = 2(x - 4)^{(x + 7)} - 4 \]
Putting it all together, the equation after the transformations is:
\[ Y = 2(x - 4)^{(x + 7)} - 4 \]
Thus, the final answer after the transformations is:
\[ Y = 2(x - 4)^{(x + 7)} - 4 \]
So we can express it with the arrow notation:
\[ Y = 4(x-4)^{(x+7)} - 6 \rightarrow Y = 2(x - 4)^{(x + 7)} - 4 \]