Math Problem Statement

f(x)+3 state the transformation

Solution

The function f(x)+3f(x) + 3 represents a vertical translation of the graph of f(x)f(x).

Transformation:

  • The graph of f(x)f(x) is shifted upward by 3 units.

This means that for every point (x,y)(x, y) on the graph of f(x)f(x), the new point on the graph of f(x)+3f(x) + 3 will be (x,y+3)(x, y + 3).

Would you like more details on vertical translations or transformations in general?

Here are 5 related questions you might find useful:

  1. What is a horizontal translation of a function?
  2. How do vertical and horizontal shifts differ in transformations?
  3. How does adding or subtracting a constant inside the function affect the graph?
  4. What is a reflection transformation in functions?
  5. Can a function be stretched or compressed, and how would that affect the graph?

Tip: To determine the direction of a transformation (up, down, left, or right), think about whether you're adding or subtracting inside or outside the function.

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Math Problem Analysis

Mathematical Concepts

Functions
Vertical Translation
Graph Transformations

Formulas

f(x) + 3

Theorems

Transformation of functions

Suitable Grade Level

Grades 9-11