Question

Give the equation transformed from fx=1/x, reflected about the x-axis followed by a translation right 9 and down 7 units.

Answer 1

The transformed function after reflecting f(x) = 1/x about the x-axis and translating it right 9 and down 7 units is j(x) = -1/(x - 9) - 7.

Step-by-step explanation:

To find the transformed equation of the function f(x) = 1/x after it is reflected about the x-axis, followed by a translation right 9 units and down 7 units, we follow these steps:

• Reflect f(x) about the x-axis by multiplying the function by -1, giving us g(x) = -1/x.
• Translate g(x) right 9 units by replacing x with (x - 9), resulting in h(x) = -1/(x - 9).
• Finally, translate h(x) down 7 units by subtracting 7 from the function, which gives us the final equation: j(x) = -1/(x - 9) - 7.

Therefore, the transformed function is j(x) = -1/(x - 9) - 7.