Final answer:
To shrink the graph of f(x)=2x³ horizontally by a factor of 5, the value of k in the transformation f(kx) is 1/5. The correct answer is B) k=1/5.
Step-by-step explanation:
To determine the value of k in the transformation f(kx) that will shrink the graph of f(x)=2x³ horizontally by a factor of 5, we must multiply the x-values by a factor greater than 1. If the graph of a function is shrunk horizontally by a factor of 5, it means that each x-value is being multiplied by 5 in the transformed function.
Therefore, the value of k that accomplishes this is 5 because it will stretch the x-values by that factor, making them appear 5 times closer together.
To shrink the graph of f(x)=2x³ horizontally by a factor of 5, we need to find the value of k in the transformation f(kx).
The horizontal shrink factor is the reciprocal of the vertical stretch factor, so the value of k is equal to 1/5.
Therefore, the correct answer is A) k=1/5.