Math Problem Statement

Construct a table of values and sketch the graph of the following functions: f(x) = 1/x, F(x) = 1/(x - 2), g(x) = x/(x + 1), G(x) = 2/(x - 2)^2.

Solution

The image contains four functions for which you are asked to construct a table of values and sketch their graphs. The functions are:

  1. f(x)=1xf(x) = \frac{1}{x}
  2. F(x)=1x2F(x) = \frac{1}{x - 2}
  3. g(x)=xx+1g(x) = \frac{x}{x + 1}
  4. G(x)=2(x2)2G(x) = \frac{2}{(x - 2)^2}

To proceed:

  1. Construct a table of values: For each function, choose a set of values for xx, calculate the corresponding y=f(x)y = f(x), and then create a table of the points.
  2. Sketch the graph: Plot the points on a coordinate system and draw the curve for each function based on their behavior (e.g., asymptotes, intercepts).

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Math Problem Analysis

Mathematical Concepts

Functions
Asymptotes
Rational Functions
Graphing

Formulas

f(x) = 1/x
F(x) = 1/(x - 2)
g(x) = x/(x + 1)
G(x) = 2/(x - 2)^2

Theorems

Asymptote Theorem
Graphing Rational Functions

Suitable Grade Level

Grades 9-12