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, let's break it down step by step:
1. Start with the equation f(x) = x^3. This is a cubic function, which means it has a characteristic "S" shape.
2. The graph of g(x) is obtained by applying two transformations to f(x): a horizontal compression by a factor of 1/2 and a reflection across the x-axis.
3. The horizontal compression means that every x-coordinate of f(x) will be multiplied by 1/2 in the equation g(x) = -(2x)^3. This results in the graph of g(x) being narrower than the graph of f(x).
4. The reflection across the x-axis means that the positive and negative values of f(x) will be flipped in g(x). In other words, any point that was above the x-axis in f(x) will be below the x-axis in g(x), and vice versa.
5. Combining the horizontal compression and reflection, you get the graph of g(x) = -(2x)^3, which is a compressed and vertically flipped version of f(x) = x^3.
So, in summary, the graph of g(x) = -(2x)^3 is a horizontally compressed and vertically reflected version of the graph of f(x) = x^3.