Pregunta
Use transformations of the absolute value function,
What transformations are needed in order to obtain the graph of
of
Use the graphing tool to graph the equation.
What transformations are needed in order to obtain the graph of
of
Use the graphing tool to graph the equation.
Ask by Murphy Tyler. in the United States
Mar 25,2025
Solución de inteligencia artificial de Upstudy
Respuesta verificada por el tutor
Responder
The transformations needed are:
- Reflection about the
-axis - Vertical shift
- Horizontal shift
Solución
-
Start with the function
. -
Apply a horizontal shift to the right by 4 to obtain
.
This corresponds to option F. -
Apply a reflection about the
-axis.
This changesto which is option A. -
Apply a vertical shift upward by 6.
This shifts the graph to become, which corresponds to option B.
Thus, the transformations needed are:
- A. Reflection about the
-axis - B. Vertical shift
- F. Horizontal shift
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Simplifique esta solución Bonus Knowledge
To obtain the graph of
- Firstly, the term
indicates a reflection about the -axis (Option A). This flips the graph upside down. - The
in the absolute value represents a horizontal shift to the right by 4 units (Option F). - Finally, the
indicates a vertical shift upwards by 6 units (Option B).
So, the correct transformations are A, B, and F!
Now, let’s dive into some engaging additional knowledge:
Transformations of functions can be visualized as a series of “moves” you make on the graph. If you picture the original absolute value graph like a cozy mountain peak, then reflecting it flips it upside down like turning the peak into a valley. Horizontal and vertical shifts are like moving that valley around on a map, ensuring it finds the perfect spot to hang out!
If you want to get better at understanding these transformations, a good idea is to practice with different base functions. Turn up the fun by using graphing software or apps to visualize how changing parameters affects the shape and position of graphs. Seeing is believing, and it makes for a fantastic way to grasp these concepts!
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