Math Problem Statement

Given the graphed function below, which of the following ordered pairs are found on the inverse function?

Solution

The problem asks which ordered pairs from the options are found on the inverse of the graphed function. To solve this, let's go over how to find points on the inverse function.

Steps to solve:

  1. Understanding the inverse function:

    • If a point (x,y)(x, y) is on the original function, then (y,x)(y, x) will be on the inverse function.
  2. Identifying key points:

    • We observe the graph and determine a few points clearly visible on the function. These will help us find their inverses.
  3. Determine the corresponding inverse points:

    • Check each option and see if the points on the graph (visually identified) match the inverses of any given pairs.

Let's check a few potential points from the graph of the function. Then, I'll compare with the answer choices.

From the graph:

  • The graph appears to have points like (1,0)(1, 0) and (1,0)(-1, 0) based on the axis intersections. So, the inverse points would be (0,1)(0, 1) and (0,1)(0, -1).

Now, let's analyze each answer choice to determine which points would match these inverse pairs.

I'll verify the specific points and compare them to the answer options now.Based on the comparison:

  • Option B and Option C contain ordered pairs that match points on the inverse of the graph.

Thus, both B and C are correct answers.

Would you like further details or have any questions?

Here are some related questions:

  1. How do you find the inverse of a linear function?
  2. What conditions must a function satisfy to have an inverse?
  3. Can you determine the domain and range of the inverse function from the original function's graph?
  4. How would you solve for the inverse algebraically?
  5. Can a function's inverse be determined visually from its symmetry?

Tip: Always remember that the graph of a function and its inverse are symmetric with respect to the line y=xy = x.

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Math Problem Analysis

Mathematical Concepts

Inverse Functions
Graphing
Algebra

Formulas

(x, y) on the function implies (y, x) on the inverse

Theorems

A function's inverse is symmetric to the original function across the line y = x

Suitable Grade Level

Grades 9-12