Question

write a function g whose graph represents the indicated transformations of the graph of f. f(x)=-2|2x+4|+5 Let g be a horizontal stretch by a factor of 4 followed by a reflection in the x-axis and then a translation 3 units left, and finally a vertical shrink by a factor of 1/3.

Answer 1

The function g(x) that represents the indicated transformations of the graph of f(x) = -2|2x + 4| + 5 would involve a series of transformations. Let's break down each step:

1. Horizontal stretch by a factor of 4: Multiply x by 1/4.
2. Reflection in the x-axis: Multiply the entire function by -1.
3. Translation 3 units left: Add 3 to x.
4. Vertical shrink by a factor of 1/3: Multiply the entire function by 1/3.

Putting it all together, the function g(x) can be written as:

g(x) = (1/3) * (-1) * -2 * |2 * (x + 3)| + 5

Simplifying:

g(x) = (2/3) * |2 * (x + 3)| + 5

This function g(x) represents the transformations of f(x) as described. (I think)