Math Problem Statement

Find the zero of the function.

Find the zero of the function.

Solution

The function given in the image is:

y=x+5y = |x + 5|

To find the zero of the function, we need to determine the value of xx that makes y=0y = 0.

For the absolute value function, y=x+5y = |x + 5|, the function equals zero when the expression inside the absolute value is zero:

x+5=0x + 5 = 0

Solving for xx:

x=5x = -5

So, the zero of the function is x=5x = -5.

Would you like further details or have any questions? Here are five related questions you might find useful:

  1. What is the general form of an absolute value function?
  2. How do you find the zero of a function with absolute values?
  3. What are the properties of the absolute value function?
  4. How would the graph of y=x+5y = |x + 5| look?
  5. Can an absolute value function have more than one zero?

Tip: When dealing with absolute value functions, always consider the point where the expression inside the absolute value becomes zero, as it often indicates a critical point such as a zero or vertex of the graph.

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Math Problem Analysis

Mathematical Concepts

Algebra
Absolute Value Functions

Formulas

y = |x + 5|

Theorems

Property of Absolute Value

Suitable Grade Level

Grades 8-10