Question

Translate the equation 2 units to the left. Then reflect across the x-axis
Y=-(-2)^x then arrow sign

Answer 1

To translate the equation \( Y = -(-2)^x \) 2 units to the left, we will replace \( x \) with \( x + 2 \). This gives us the new equation:

\[
Y = -(-2)^{(x + 2)}
\]

Next, to reflect this equation across the x-axis, we multiply the entire equation by -1. This results in:

\[
Y = -(-(-2)^{(x + 2)}) = -(-2)^{(x + 2)}
\]

Thus, the final equation after both transformations is:

\[
Y = (-2)^{(x + 2)}
\]

So the transformations yield:

\[
Y = -(-2)^{(x + 2)} \rightarrow Y = -(-2)^{(x + 2)}
\]

Therefore, if you're applying an arrow sign to indicate the transformation process, it can be visually represented as:

\[
Y = -(-2)^x \rightarrow Y = -(-2)^{(x + 2)} \rightarrow Y = (-2)^{(x + 2)}
\]