Use transformations of the absolute value function, , to graph the function
.
What transformations are needed in order to obtain the graph of from the graph
of ? Select all that apply.
A. Horizontal shift
B. Reflection about the -axis
C. Vertical stretch/shrink
D. Reflection about the -axis
E. Horizontal stretch/shrink
F. Vertical shift
Use the graphing tool to graph the equation.
D.

Ask by Rodriguez Delgado. in the United States

Mar 25,2025

Question

Use transformations of the absolute value function, , to graph the function
.
What transformations are needed in order to obtain the graph of from the graph
of ? Select all that apply.
A. Horizontal shift
B. Reflection about the -axis
C. Vertical stretch/shrink
D. Reflection about the -axis
E. Horizontal stretch/shrink
F. Vertical shift
Use the graphing tool to graph the equation.
D.

Ask by Rodriguez Delgado. in the United States

Mar 25,2025

UpStudy AI · Accepted Answer

1. Start with the base function $$ f(x) = |x| $$.

2. The function to graph is $$ g(x) = -|x-4| -1 $$.

3. The transformation steps are:

- **Horizontal Shift:**  
     The expression $$ |x-4| $$ indicates a shift to the right by 4 units.
   
   - **Reflection about the $$ x $$-axis:**  
     The negative sign in front of the absolute value, $$ -|x-4| $$, reflects the graph across the $$ x $$-axis.
   
   - **Vertical Shift:**  
     The term $$-1$$ at the end shifts the graph downward by 1 unit.

4. The necessary transformations are:
   - $$ \square $$ A. Horizontal shift
   - $$ \square $$ B. Reflection about the $$ x $$-axis
   - $$ \square $$ F. Vertical shift
The transformations needed are: - Horizontal shift - Reflection about the $$ x $$-axis - Vertical shift

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