I can help you with your math question.
The sequence of transformations on f(x) = 1/x is:
- Reflect f(x) across the x-axis
- Shift f(x) left 2 units
- Stretch f(x) vertically by a factor of 3
- Shift f(x) up 5 units
To write down a formula for g(x), we need to apply these transformations in the reverse order. That is:
- Start with f(x) = 1/x
- Shift it down 5 units: f(x) - 5 = 1/x - 5
- Compress it vertically by a factor of 3: (f(x) - 5)/3 = (1/x - 5)/3
- Shift it right 2 units: (f(x) - 5)/3 + 2 = (1/x - 5)/3 + 2
- Reflect it across the x-axis: -(f(x) - 5)/3 + 2 = -(1/x - 5)/3 + 2
Therefore, the formula for g(x) is:
g(x) = -(1/x - 5)/3 + 2
Patrick's answer of g(x) = 2x + 5 is incorrect because he did not apply the transformations correctly. He made the following mistakes:
- He multiplied f(x) by 2 instead of dividing it by 3, which changed the shape of the graph from a hyperbola to a line.
- He added 5 to x instead of subtracting it, which shifted the graph in the wrong direction.
- He did not reflect the graph across the x-axis, which changed the sign of the function.
I hope this helps you understand how to write down a formula for a transformed function. If you have any more questions, feel free to ask me.
Explanation: