Find solutions to your questions with the help of IDNLearn.com's expert community. Our platform provides prompt, accurate answers from experts ready to assist you with any question you may have.
Sagot :
To understand the effect on the graph of [tex]\( f(x) = x^2 \)[/tex] when it is transformed to [tex]\( h(x) = \frac{1}{5} x^2 + 12 \)[/tex], let's break down the transformations step by step.
1. Vertical Compression:
- The term [tex]\( \frac{1}{5} x^2 \)[/tex] indicates a vertical compression.
- A vertical compression occurs when the y-values of the graph are reduced.
- Since the new equation has [tex]\( \frac{1}{5} \)[/tex] as a coefficient of [tex]\( x^2 \)[/tex], the graph is vertically compressed by a factor of 5.
2. Vertical Shift:
- The term [tex]\( +12 \)[/tex] in [tex]\( h(x) = \frac{1}{5} x^2 + 12 \)[/tex] indicates a vertical shift.
- Adding 12 to the function shifts the entire graph up by 12 units.
Now, let’s summarize these transformations:
- The graph is vertically compressed by a factor of 5 due to the [tex]\( \frac{1}{5} \)[/tex] multiplier.
- The graph is shifted vertically upwards by 12 units due to the [tex]\( +12 \)[/tex].
Therefore, the correct description of the transformation is:
C. The graph of [tex]\( f(x) \)[/tex] is vertically compressed by a factor of 5 and shifted 12 units up.
1. Vertical Compression:
- The term [tex]\( \frac{1}{5} x^2 \)[/tex] indicates a vertical compression.
- A vertical compression occurs when the y-values of the graph are reduced.
- Since the new equation has [tex]\( \frac{1}{5} \)[/tex] as a coefficient of [tex]\( x^2 \)[/tex], the graph is vertically compressed by a factor of 5.
2. Vertical Shift:
- The term [tex]\( +12 \)[/tex] in [tex]\( h(x) = \frac{1}{5} x^2 + 12 \)[/tex] indicates a vertical shift.
- Adding 12 to the function shifts the entire graph up by 12 units.
Now, let’s summarize these transformations:
- The graph is vertically compressed by a factor of 5 due to the [tex]\( \frac{1}{5} \)[/tex] multiplier.
- The graph is shifted vertically upwards by 12 units due to the [tex]\( +12 \)[/tex].
Therefore, the correct description of the transformation is:
C. The graph of [tex]\( f(x) \)[/tex] is vertically compressed by a factor of 5 and shifted 12 units up.
Thank you for using this platform to share and learn. Don't hesitate to keep asking and answering. We value every contribution you make. For trustworthy answers, rely on IDNLearn.com. Thanks for visiting, and we look forward to assisting you again.