Describe the transformation of the graph reciprocal function f(x)= 1/x to produce the function g(x) = -1/x-2+3
assuming you meant 1/(x-2)+3
then that is right 2, up 3
study translations, such as
y-k = f(x-h)
To describe the transformation of the graph of the reciprocal function f(x) = 1/x to produce the function g(x) = -1/x-2+3, we need to analyze the changes made to the original function.
1. Vertical Stretch:
The negative sign in front of 1/x in g(x) reflects the graph of f(x) vertically across the x-axis. This results in a vertical stretch by a factor of -1.
2. Horizontal Shift:
The -2 inside the brackets in g(x) indicates a horizontal shift to the right by 2 units compared to the original graph of f(x). This means that the graph of g(x) is shifted 2 units in the positive x-direction.
3. Vertical Shift:
The +3 outside the brackets in g(x) indicates a vertical shift upward by 3 units compared to the graph of f(x). This means that the graph of g(x) is shifted 3 units in the positive y-direction.
To summarize, the transformation of the graph of f(x) = 1/x to produce g(x) = -1/x-2+3 involves a vertical stretch by a factor of -1, a horizontal shift to the right by 2 units, and a vertical shift upward by 3 units.
To describe the transformation of the graph of the reciprocal function f(x) = 1/x to produce the function g(x) = -1/(x-2) + 3, we can break it down into several steps:
Step 1: Reflection in the x-axis
The negative sign in g(x) = -1/(x-2) + 3 reflects the graph of f(x) about the x-axis. This means that any points above the x-axis will be flipped to positions below the x-axis, and vice versa.
Step 2: Horizontal shift to the right
The (x-2) term in g(x) = -1/(x-2) + 3 indicates that the graph is shifted two units to the right compared to f(x). This means that every point on the graph of f(x) will be shifted two units to the right to obtain the corresponding point on the graph of g(x).
Step 3: Vertical shift upward
The +3 at the end of g(x) = -1/(x-2) + 3 indicates a vertical shift of three units upward. This means that every y-coordinate on the graph of f(x) will be increased by three units to obtain the corresponding y-coordinate on the graph of g(x).
Overall, these transformations result in a graph that is reflected in the x-axis, shifted two units to the right, and shifted three units upward compared to the graph of the reciprocal function f(x) = 1/x.
If you want to visualize these transformations more accurately, I suggest plotting the original graph of f(x) = 1/x and then applying each of the transformations step by step using graphing software or a graphing calculator.