Question

Write a function g whose graph represents the indicated transformation of the graph of f.

f(x) = |3x + 8|- 7; reflection in the x-axis.

Answer 1

To reflect the graph of a function in the x-axis, we can apply the transformation y = -f(x). Since f(x) = |3x + 8| - 7, the function g(x) = -|3x + 8| + 7 represents the reflection of the graph of f(x) in the x-axis.

Step-by-step explanation:

To reflect the graph of a function in the x-axis, we can apply the transformation y = -f(x). Since f(x) = |3x + 8| - 7, we have g(x) = -(|3x + 8| - 7). To simplify further, we can rewrite g(x) as g(x) = -|3x + 8| + 7.

Let's break down the transformation step by step:

1. The absolute value function |3x + 8| reflects the right-side portion of the graph about the y-axis. So, we have -|3x + 8|.
2. The subtraction of 7 shifts the entire graph vertically downwards by 7 units.
3. Finally, the negative sign before |3x + 8| reflects the graph once more in the x-axis, which completes the transformation.

Therefore, the function g(x) = -|3x + 8| + 7 represents the reflection of the graph of f(x) = |3x + 8| - 7 in the x-axis.