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What transformation occurs when you go from [tex]f(x) = 2x[/tex] to [tex]h(x) = 2x - 3[/tex]?

A. The graph shifts to the left 3 units
B. The graph shifts to the right 3 units
C. The graph shifts up 3 units
D. The graph shifts down 3 units

Sagot :

GinnyAnsweridn
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
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