Math Problem Statement

The graph of a function is given. Graph the inverse function.

Solution

The image you uploaded shows a graph of a function along with an instruction to graph its inverse function.

To graph the inverse of a function, you can follow these steps:

  1. Reflect over the line y=xy = x: The inverse function is a reflection of the original function across the line y=xy = x. This means that for each point (x,y)(x, y) on the original function, the point (y,x)(y, x) will be on the inverse function.

  2. Find key points on the graph: Identify important points on the original graph, like intercepts and any significant coordinates.

  3. Swap the x and y coordinates: Once you've identified these points, swap the x and y coordinates for each point to form the inverse.

  4. Plot the new points: Graph these swapped coordinates on the same coordinate plane.

  5. Draw the line of reflection: You may also want to sketch the line y=xy = x for reference, as the inverse should be symmetric with respect to this line.

Would you like me to assist further with specific steps in finding the inverse or need help with any other part of the graph?

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Math Problem Analysis

Mathematical Concepts

Graphing Functions
Inverse Functions
Reflection

Formulas

y = x (Line of reflection)

Theorems

Inverse Function Theorem

Suitable Grade Level

Grades 9-11