Graph the given​ functions, f and​ g, in the same rectangular coordinate system. Describe how the graph of g is related to the graph of f.
f left parenthesis x right parenthesis
equals
StartAbsoluteValue x EndAbsoluteValue
​g(x)
equals
StartAbsoluteValue x EndAbsoluteValueplus5

The graph of \( f(x) = |x| \) is the standard V-shaped absolute value function, while the graph of \( g(x) = |x| + 5 \) is the same V-shaped function, but shifted 5 units upward. 

### Relationship:
The graph of \( g(x) \) is a vertical translation of \( f(x) \). Specifically, \( g(x) \) is obtained by moving the graph of \( f(x) \) up by 5 units. 

Do you want more details or have any questions?

Here are some related questions for further exploration:
1. How would the graph of \( g(x) = |x| - 3 \) compare to \( f(x) \)?
2. What happens if you subtract a constant from \( |x| \), e.g., \( f(x) = |x| - 2 \)?
3. How would the graph change if you multiply \( |x| \) by a constant, say \( 2|x| \)?
4. What is the effect of adding or subtracting from the \( x \)-variable inside \( |x| \)?
5. How does the vertex of \( f(x) = |x| \) shift with vertical or horizontal translations?

**Tip**: Vertical shifts occur when constants are added or subtracted to the entire function.

Graph the given functions, f and g, in the same rectangular coordinate system. Describe how the graph of g is related to the graph of f. f(x) = |x|, g(x) = |x| + 5.

Learn how to graph the absolute value functions f(x) = |x| and g(x) = |x| + 5. This problem explains the vertical translation of absolute value functions and is suitable for students in Grades 9-10. Includes a step-by-step description of the relationship between the two graphs.

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