Question
Reflect across the x-axis, then translate up 5 units
Y=-8x+7 arrow sign
Y=-8x+7 arrow sign
Answers
GPT-4o mini
To reflect the function \( y = -8x + 7 \) across the x-axis, you negate the entire output \( y \). This changes the equation to:
\[
y = -(-8x + 7) = 8x - 7
\]
Next, to translate this new equation \( y = 8x - 7 \) up by 5 units, you add 5 to the output \( y \):
\[
y = 8x - 7 + 5 = 8x - 2
\]
So, the final result after first reflecting across the x-axis and then translating up by 5 units is:
\[
y = 8x - 2
\]
\[
y = -(-8x + 7) = 8x - 7
\]
Next, to translate this new equation \( y = 8x - 7 \) up by 5 units, you add 5 to the output \( y \):
\[
y = 8x - 7 + 5 = 8x - 2
\]
So, the final result after first reflecting across the x-axis and then translating up by 5 units is:
\[
y = 8x - 2
\]