State the transformation for g(x) = -2 (2x - 4)³ - 1
Would it be
a vertical stretch by a factor of 2
a reflection in the x-axis
a horizontal stretch by a factor of 1/2
a translation 4 units right and 1 unit down
Am i right?
try changing it to this:
g(x)= -2(8)(x-2)^3 -1
= -16(x-2)^3 -1
does that change your analysis?
Yes, you are correct! Let's break down the given transformation, g(x) = -2 (2x - 4)³ - 1, and determine each component.
1. Vertical Stretch by a factor of 2:
The -2 in front of the expression inside the parentheses, (-2), represents a vertical stretch by a factor of 2. This means that the graph of the function will be stretched vertically, making it taller.
2. Reflection in the x-axis:
The negative sign in front of the entire expression, -2 (2x - 4)³ - 1, represents a reflection in the x-axis. This means that the graph of the function will be flipped upside down.
3. Horizontal Stretch by a factor of 1/2:
The expression inside the parentheses, (2x - 4), represents a horizontal stretch. In this case, the coefficient 2 will cause the graph to be compressed horizontally by a factor of 1/2. This means that the graph will become narrower.
4. Translation 4 units right and 1 unit down:
The -4 and -1 outside the parentheses represent a translation of the graph. The -4 will shift the graph 4 units to the right, and the -1 will shift it 1 unit down.
So, overall, the transformation for g(x) = -2 (2x - 4)³ - 1 includes a vertical stretch by a factor of 2, a reflection in the x-axis, a horizontal stretch by a factor of 1/2, and a translation 4 units to the right and 1 unit down.