Final Answer:
g(x) = |x| + 4; horizontal shrink by a factor of 1/2.
Step-by-step explanation:
To achieve a horizontal shrink by a factor of 1/2, we modify the argument inside the absolute value function. The transformation involves replacing "x" with "x/2" inside the absolute value function. Therefore, the function representing the desired transformation is
. This effectively compresses the graph horizontally by a factor of 1/2.
In the original function
, the coefficient of "x" inside the absolute value function is 2, which causes a horizontal stretch by a factor of 2. To counteract this stretch, we introduce the horizontal shrink by dividing "x" by 2 inside the absolute value function. The constant term "+4" remains unchanged since it represents a vertical shift.
Graphically, this transformation compresses the graph horizontally, making it narrower compared to the original function. Checking the result using a graphing calculator will confirm the desired horizontal shrinkage, demonstrating that
appropriately transforms
as required.