How is the graph of g(x)= -(2x)^3 related to the graph pf f(x) = x^3
answer: I don't understand the answer..thank you
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, we need to analyze the transformations applied to the original function f(x) to obtain g(x).
Let's start with the graph of f(x) = x^3. The graph of this function is a cubic function, which means it has a shape like the letter "S" when plotted on a coordinate plane.
Now, let's look at the transformation applied to f(x) to obtain g(x):
1. Horizontal Compression: The factor 2 in front of x in g(x) indicates a horizontal compression. This means that the graph of g(x) will be narrower than f(x) by a factor of 1/2. In other words, the graph of g(x) will be squeezed horizontally.
2. Reflection across the x-axis: The negative sign in front of (2x)^3 in g(x) indicates a reflection across the x-axis. This means that all the points on the graph of g(x) will be reflected to the other side of the x-axis. The positive values of y on the graph of f(x) will become negative values on the graph of g(x), and vice versa.
Combining these transformations, the graph of g(x) = -(2x)^3 will have a similar shape to the graph of f(x) = x^3, but it will be narrower horizontally and reflected across the x-axis.
I hope this explanation clarifies the relationship between the two graphs. Let me know if you have any further questions!