Question

10.) f(x) = - | x + 1 Transformation 1: Transformation 2: 12.) f(x) = 7|x - 3] - 4 Transformation 1: Transformation 2: Transformation 3:

Answer 1

The question asks to determine the transformations of two absolute value functions. Transformations include reflections, vertical stretches, horizontal shifts, and vertical shifts.

Step-by-step explanation:

The question concerns transformations of absolute value functions in mathematics. Specifically, it asks to identify the transformations applied to two different absolute value functions, f(x) = - |x + 1| and f(x) = 7| x - 3| - 4.

For the first function, one common transformation could be a reflection across the x-axis due to the negative sign outside the absolute value. For the second function, there are three transformations to be identified. The '7' represents a vertical stretch by a factor of 7, the '|x - 3|' represents a horizontal shift 3 units to the right, and the '-4' represents a vertical shift 4 units downwards.

Answer 2

In the first question, we are given the transformed function

f(x) = - | x | + 1

and we are asked what was the first transformation and the second one of the original expresion f(x) = | x |

The first transformation is the multiplication by -1 of the x-variable, which involves a reflection around the x-axis. and the second transformation is a vertical shiftup in one (1) unit.

Transf 1 : reflection around x-axis

Transf 2: vertical shift in one unit

Second problem.

We are given the transformed function

f(x) = 7 |x - 3| - 4

so the first transformation is the subtraction of "3" from the "x" variable, which involves a horizontal shift to the right in 3 units

the second transformation is the product by 7 outside the absolute value symbol. This accounts for a vertical stretching by a factor of "7".

The last transformation is the subtraction of 4 ate the end. This accounts for a vertical shift of 4 units down.

Transf 1: horizontal shift 3 units to the right

Transf 2: vertical stretching by a factor of 7

Transf 3: vertical shift of 4 units down.