Question

for each circled number in the picture, use the drop - down option below to select the transformation it causes to the graph. f(x)=-3|x - 4|+1 1) select answer 2) select answer 3) select answer 4) select answer

Explanation:

Step1: Analyze the - 3

The coefficient - 3 in front of the absolute - value function $|x - 4|$ causes a vertical stretch by a factor of 3 and a reflection across the x - axis.

Step2: Analyze the - 4 inside the absolute - value

The value $x-4$ inside the absolute - value function $|x - 4|$ causes a horizontal shift of 4 units to the right.

Step3: Analyze the + 1 outside

The + 1 outside the absolute - value function $|x - 4|$ causes a vertical shift of 1 unit up.

Assuming the circled numbers correspond to the coefficients and constants in order:

1. If circled number 1 is - 3: Reflection across the x - axis and vertical stretch by a factor of 3.
2. If circled number 2 is - 4: Horizontal shift 4 units to the right.
3. If circled number 3 is the absolute - value symbol (not a number for transformation analysis in the traditional sense here, but if we consider it as part of the base function structure).
4. If circled number 4 is + 1: Vertical shift 1 unit up.

Answer:

1. Reflection across the x - axis and vertical stretch by a factor of 3
2. Horizontal shift 4 units to the right
3. N/A (not a transformation - causing number in the relevant sense)
4. Vertical shift 1 unit up