Question

Discribe a series of transformations of the graph of f(x)=x that results in the graph of g(x)= -x+6

Answer 1

To transform the graph of f(x)=x to g(x)=-x+6, reflect f(x) across the x-axis to get h(x)=-x, then translate h(x) up by 6 units to obtain g(x).

Step-by-step explanation:

The question asks about the series of transformations that could be applied to the graph of the function f(x) = x to obtain the graph of the function g(x) = -x + 6. Here's how we can transform f(x) to g(x):

• Reflect f(x) across the x-axis. This changes f(x) = x to h(x) = -x. Reflection across the x-axis inverts the sign of the y-coordinates, and since the original graph is a straight line with a 45-degree angle, this reflection just flips it over the x-axis.
• Then, translate h(x) up by 6 units. This adds 6 to each of its y-coordinates, changing h(x) = -x to g(x) = -x + 6.

The final graph of g(x) will have the same linearity as f(x), but it will be reflected and shifted up.

Answer 2

the transformation is entered as y= is the transformation