Question

5ˣ translated 2 units down and reflection in the y-axis

Answer 1

The expression 5ˣ translated 2 units down and reflected in the y-axis can be represented as
`-5^((x+2)).`

Step-by-step explanation:

To translate a function downward, we subtract the translation value from the original function. In this case, the original function is 5ˣ, and the translation is 2 units down. Therefore, we subtract 2 from the exponent, resulting in
`5^((x-2))`.

Next, to reflect the function in the y-axis, we negate the entire expression. The negation of
`5^((x-2))` is -
`5^((x-2))`. This reflects the function in the y-axis, changing the sign of the entire expression.

Combining the translation and reflection, we get -
`5^((x-2))` as the final expression. This means the original function 5ˣ, when translated 2 units down and reflected in the y-axis, is represented by -
`5^((x-2))`.

In mathematical terms, the translation is denoted by a shift in the exponent, and the reflection is denoted by the negative sign. The process is systematic: first, perform the translation, and then apply the reflection. This approach ensures an accurate transformation of the original function based on the given specifications.