To determine the transformation that occurs when you go from [tex]\( f(x) = 2x \)[/tex] to [tex]\( h(x) = 2x - 3 \)[/tex], let's analyze the function step by step.
1. Identify the original function and the transformed function:
- The original function is [tex]\( f(x) = 2x \)[/tex].
- The transformed function is [tex]\( h(x) = 2x - 3 \)[/tex].
2. Determine the type of transformation:
- The transformation involves the subtraction of 3 from the function [tex]\( f(x) \)[/tex]. When a constant is subtracted from a function, it results in a vertical shift downward.
3. Detail the effect of the transformation:
- For the function [tex]\( f(x) \)[/tex], each output value of [tex]\( f(x) \)[/tex] is multiplied by 2.
- When transitioning to [tex]\( h(x) \)[/tex], each output value of [tex]\( 2x \)[/tex] is then reduced by 3.
- This reduction causes the entire graph of [tex]\( f(x) = 2x \)[/tex] to move downward by 3 units.
4. Conclusion:
- The transformation [tex]\( h(x) = 2x - 3 \)[/tex] results in the graph of the original function [tex]\( f(x) = 2x \)[/tex] moving downward by 3 units.
Thus, the correct answer is:
d) The graph shifts down 3 units
