I don't understand the answer..thank you
How is the graph of g(x)= -(2x)^3 related to the graph pf f(x) = x^3
answer:
the graph of g(x) is a horizontal compression of the graph of f(x) by a factor of 1/2 and a reflection across the x axis.
To understand how the graph of g(x) = -(2x)^3 is related to the graph of f(x) = x^3, let's break it down step by step.
1. Start with the original function f(x) = x^3. This function is a simple cubic function, which means that for each value of x, the corresponding y-value is obtained by cubing x.
2. Now, let's analyze the function g(x) = -(2x)^3. The first thing to note is the negative sign outside the parentheses: -(2x)^3. This indicates that the graph of g(x) will be reflected across the x-axis compared to the graph of f(x).
3. Next, let's focus on the expression inside the parentheses, (2x). This means that the graph of g(x) will be horizontally compressed compared to the graph of f(x). In other words, the points on the graph of g(x) will appear closer to the y-axis than the corresponding points on the graph of f(x). This compression factor of 2 means that for each x-value, the corresponding y-value will be obtained by cubing (2x).
Combining the reflection across the x-axis and the horizontal compression by a factor of 2, we can conclude that the graph of g(x) = -(2x)^3 is a horizontally compressed and reflected version of the graph of f(x) = x^3.
I hope this explanation clarifies the relationship between the two functions.