Math Problem Statement

Plot the inverse of the function shown on the grid.

Solution

The problem asks you to plot the inverse of the given function on the grid. Let's break this down:

  1. The graph of the function shows three points that are important to focus on:
    • The point (2,2)(2, 2)
    • The point (4,0)(4, 0)
    • The point (6,2)(6, -2)

To find the inverse of a function, you simply swap the x- and y-coordinates of each point. So the inverse points will be:

  • The inverse of (2,2)(2, 2) is (2,2)(2, 2) (this stays the same since x = y).
  • The inverse of (4,0)(4, 0) is (0,4)(0, 4).
  • The inverse of (6,2)(6, -2) is (2,6)(-2, 6).

Now, plot these points on the new grid:

  • Mark the point (2,2)(2, 2).
  • Mark the point (0,4)(0, 4).
  • Mark the point (2,6)(-2, 6).

After plotting the points, connect them to form the graph of the inverse function. You can use a line tool or dot tool, as per the options given in the interface, to draw this.

Would you like further clarification or detailed steps on plotting the graph?

Here are some follow-up questions:

  1. What is the general process for finding the inverse of a function?
  2. How can you confirm if a function has an inverse?
  3. What is the significance of the line y=xy = x in graphing inverses?
  4. What transformations occur when switching from a function to its inverse?
  5. How can the concept of inverse functions be applied in real-life contexts?

Tip: Always ensure the function is one-to-one before attempting to find its inverse. This ensures the inverse is also a function.

Ask a new question for Free

By Image

Drop file here or Click Here to upload

Math Problem Analysis

Mathematical Concepts

Inverse functions
Graphing
Coordinate Geometry

Formulas

To find the inverse of a function, swap the x- and y-coordinates of each point.

Theorems

Inverse Function Theorem

Suitable Grade Level

Grades 9-12