Answer:
To get black from red ...
- scale by a factor of 3
- reflect over the x-axis
- shift left 1 unit
- shift up 4 units
Explanation:
You want the know the transformation that is applied to the red graph to make it be the black graph.
Observation
We note that the vertex of the black graph is (-1, 4), which is 1 unit left and 4 units up from the vertex of the red graph.
The black graph opens downward, and has a slope of ±3 compared to the slope of ±1 for the red graph. This means it has been reflected across the x-axis and scaled by a factor of 3.
Transformation
The reflection and scaling can both be accomplished by multiplying the function by -3. The translation is accomplished by adding 4 to the function value to shift it up 4 units, and adding 1 to the x-value to shift the graph left 1 unit.
The transformations applied to the red graph are ...
- scale by a factor of 3
- reflect over the x-axis
- shift left 1 unit
- shift up 4 units