Math Problem Statement

/graph the function y = f(x)+ 2

Solution

To graph the function y=f(x)+2y = f(x) + 2, follow these steps:

  1. Start with the graph of y=f(x)y = f(x):

    • This is the original function you are given. You can plot this function first, if known.
  2. Apply the vertical shift:

    • The function y=f(x)+2y = f(x) + 2 represents a vertical shift of the graph of y=f(x)y = f(x) by 2 units upward. This means every point on the graph of y=f(x)y = f(x) will move 2 units higher on the y-axis.

For example, if the original point on the graph of y=f(x)y = f(x) was (x1,y1)(x_1, y_1), then after the transformation it will become (x1,y1+2)(x_1, y_1 + 2).

If you want me to visualize a specific graph for f(x)f(x), you can describe the function f(x)f(x), and I can provide the graph of y=f(x)+2y = f(x) + 2 as well.

Would you like further details or any specific function for f(x)f(x)?

Here are 5 relative questions based on this topic:

  1. What is the general effect of shifting a graph vertically or horizontally?
  2. How does the transformation y=f(x)+2y = f(x) + 2 affect the symmetry of the original function?
  3. What are the differences between vertical and horizontal shifts?
  4. How would y=f(x)2y = f(x) - 2 transform the graph of f(x)f(x)?
  5. How can vertical shifts affect the domain and range of a function?

Tip: Shifting a function vertically by adding or subtracting a constant does not change the x-values; it only alters the y-values of the graph.

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Math Problem Analysis

Mathematical Concepts

Functions
Graph Transformations
Vertical Shifts

Formulas

y = f(x) + k (Vertical Shift Formula)

Theorems

Transformation of Functions

Suitable Grade Level

Grades 9-12