Math Problem Statement

Show graph of f(x)+3=|x|+3

Solution

Here's the graph of f(x)+3=x+3f(x) + 3 = |x| + 3. As you can see, the graph represents the absolute value function shifted upwards by 3 units.

Would you like further details or have any questions?

Here are five related questions to explore further:

  1. How does shifting affect the graph of an absolute value function?
  2. What would happen if we subtract 3 from both sides instead of adding 3?
  3. How does the graph of f(x)=xf(x) = |x| change if we add a constant inside the absolute value?
  4. What are some properties of the absolute value function?
  5. How can we express this function in piecewise form?

Tip: Shifting a graph vertically involves adding or subtracting a constant from the entire function, moving it up or down without affecting its shape.

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Math Problem Analysis

Mathematical Concepts

Algebra
Absolute Value Functions
Graph Transformations

Formulas

f(x) + c = |x| + c
Vertical Shifting of Functions

Theorems

Properties of Absolute Value Functions

Suitable Grade Level

Grades 9-11