Pregunta
\( \mid \leftarrow \) Use transformations of the absolute value function, \( f(x)=|x| \), to graph the function \( h(x)=-|x-4| \). What transformations are needed in order to obtain the graph of \( h(x) \) from the graph of \( f(x) \) ? Select all that apply. \( \square \) A. Reflection about the \( y \)-axis \( \square \) B. Vertical stretch/shrink \( \square \) C. Horizontal shift \( \square \) D. Vertical shift \( \square \) E. Horizontal stretch/shrink \( \square \) F. Reflection about the \( x \)-axis
Ask by Carrillo Fowler. in the United States
Feb 21,2025
Solución de inteligencia artificial de Upstudy
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To graph \( h(x) = -|x - 4| \) from \( f(x) = |x| \), perform a horizontal shift 4 units to the right and a reflection across the x-axis.
Solución
The function h(x) = –|x – 4| can be obtained from f(x) = |x| by performing the following transformations:
1. Horizontal Shift: Replace x with (x – 4) in the absolute value expression. This shifts the graph 4 units to the right.
2. Reflection about the x-axis: Multiplying the absolute value expression by – reflects the graph across the x-axis.
Thus, the correct transformations are:
C. Horizontal shift
F. Reflection about the x-axis
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Simplifique esta solución Extra Insights
To obtain the graph of \( h(x) = -|x - 4| \) from the graph of \( f(x) = |x| \), you'll need to apply a few transformations. First, you need to shift the graph horizontally to the right by 4 units, which corresponds to option C. Next, you'll reflect the graph vertically across the x-axis, which is represented by option F. The final transformations needed are a horizontal shift (to the right) and a reflection (downwards). So, options C and F are the correct choices! Happy graphing!
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