To transform the graph of [tex]\( y = 2x \)[/tex] into [tex]\( y = 2x - 4 \)[/tex], we need to understand how the functions differ.
The original equation is:
[tex]\[ y = 2x \][/tex]
The transformed equation is:
[tex]\[ y = 2x - 4 \][/tex]
Here, we can see that the new equation has a term [tex]\(-4\)[/tex] subtracted from the original equation [tex]\( y = 2x \)[/tex]. This term [tex]\(-4\)[/tex] indicates a vertical transformation.
### Identifying the Transformation:
Subtracting 4 from a function [tex]\( y \)[/tex] translates the function graph downward by 4 units. This is because each value of [tex]\( y \)[/tex] in [tex]\( y = 2x \)[/tex] is decreased by 4 units, resulting in [tex]\( y = 2x - 4 \)[/tex].
Thus, the correct statement that describes this transformation is:
- "It is the graph of [tex]\( y=2x \)[/tex] translated 4 units downward."
The other options are incorrect because:
- Translating 4 units to the right would involve modifying the x term, such as in [tex]\( y = 2(x - 4) \)[/tex].
- Translating 4 units upward would involve adding 4 instead of subtracting, resulting in [tex]\( y = 2x + 4 \)[/tex].
- Translating 2 units to the right does not match with -4 units shift in y-coordinates.
- Compressing or stretching horizontally/vertically implies a change in the coefficient of x or y, which is not the case here.
So, we select:
- "It is the graph of [tex]\( y = 2x \)[/tex] translated 4 units downward." as the correct answer.
