Hi I just got my correspondence back and the following question is wrong. Explain how the graph of f(x)=x^2-4x can be used to obtain the graph of y=g(x). Could you explain so I can see where I went so wrong. Thanks for your time.
Of course! To see how the graph of the function f(x) = x^2 - 4x can help obtain the graph of y = g(x), let's break it down step by step:
1. Start with the equation of f(x) = x^2 - 4x. This is a quadratic equation, and its graph will be a parabola.
2. To find the graph of y = g(x), we need to make a transformation of the function f(x). The transformation involves shifting the graph up, down, left, or right, and/or stretching or compressing it vertically or horizontally.
3. Suppose we want to obtain the graph of y = g(x), which is shifted up by 3 units compared to the original function f(x).
To achieve this transformation, we can modify the equation by adding 3 to it:
g(x) = f(x) + 3
= x^2 - 4x + 3
4. Now let's analyze the effect of this transformation. By adding 3 to the equation, we are shifting the entire graph of f(x) upward by 3 units. This means every point on the graph of f(x) will be shifted vertically by 3 units. The resulting graph will be the graph of y = g(x).
By plotting the points of the function g(x) = x^2 - 4x + 3, we can obtain the graph of y = g(x). You can plot points by selecting different values of x and substituting them into the equation to find the corresponding y-values. Repeat this process for multiple points and join them to create the graph.
Remember to label the axes, mark any intercepts, and highlight any important features like the vertex, axis of symmetry, and direction of the opening of the parabola.
By following these steps and understanding the transformation involved, you can obtain the graph of y = g(x) using the graph of f(x) = x^2 - 4x as a starting point.