To determine the correct description of the transformation from the graph of [tex]\( y=2x \)[/tex] to [tex]\( y=2x-4 \)[/tex], follow these steps:
1. Understanding the Original Function: The original function is [tex]\( y=2x \)[/tex], which is a straight line with a slope of 2. This means for every increase of 1 in [tex]\( x \)[/tex], [tex]\( y \)[/tex] increases by 2.
2. Introducing the Transformation: The transformed function is [tex]\( y=2x-4 \)[/tex]. Notice that the only change is the subtraction of 4 from the original function.
3. Analyzing the Effect of the Transformation:
- The term [tex]\(-4\)[/tex] subtracted from the original [tex]\( y \)[/tex] value indicates a vertical shift.
- Specifically, since it's [tex]\(-4\)[/tex], it means the graph is translated downward by 4 units.
4. Comparison to Other Possible Translations:
- If the transformation had been [tex]\( y=2x-4 \)[/tex], and we had an additional term inside the [tex]\( x \)[/tex] (e.g. [tex]\( y=2(x-4) \)[/tex]), it would indicate a horizontal translation.
- For an upward translation, the term would add a constant (e.g., [tex]\( y=2x+4 \)[/tex]).
- Horizontal compression or stretching would involve altering the coefficient of [tex]\( x \)[/tex] directly or inside a function.
Thus, the only correct description is:
- It is the graph of [tex]\( y=2x \)[/tex] translated 4 units downward.
Hence, the correct statement is:
- It is the graph of [tex]\( y=2x \)[/tex] translated 4 units downward.
