the complete question in the attached figure
y1=2x²
y2=10x²----------------- > y2=5*y1
using a graphic tool-------------------- > see the attached figure
the answer is the option A). The transformation stretches the graph by a factor of 5
Answer:
The given transformation stretches the graph by a factor of 5.
Step-by-step explanation:
We have been given that the graph of [tex]y=2x^2[/tex] is transformed into [tex]y=10x^2[/tex]. We are asked to find the effect of this transformation on the graph of the quadratic function along the y-axis.
Let us recall transformation rules for scaling:
[tex]g(x)\rightarrow ag(x)[/tex]
When [tex]a>1[/tex], the transformation stretches the graph along the y-axis by a factor of a.
When [tex]0<a<1[/tex], the transformation compresses the graph along the y-axis by a factor of a.
[tex]g(x)\rightarrow g(ax)[/tex]
When [tex]a>1[/tex], the function compressed along the x-axis by a factor of a.
When [tex]0<a<1[/tex], the function stretched along the x-axis by a factor of a.
Upon looking at our given transformation, we can see that the function is stretched along the y-axis by a factor of 5 as 10 is 5 times 2.
Therefore, our given function is stretched along the y-axis by a factor of 5.
