Question

Please Help. Functions and Relations. What is the effect on the graph of f(x)= x^2 when it is transformed to h(x)= 2x^2 + 15??

Answer 1

In general, given a function g(x), a vertical stretch/compression is given by the transformation below

$\begin{gathered} g(x)\rightarrow a*g(x) \\ a>1\rightarrow\text{ stretch} \\ 0Therefore, in our case,[tex]x^2\rightarrow2x^2\Rightarrow\text{ vertical stretch by a factor of 2}$

On the other hand, a vertical shift is given by the following transformation

$\begin{gathered} g(x)\rightarrow g(x)+b \\ b>0\rightarrow\text{ b units up} \\ b<0\rightarrow\text{ b units down} \end{gathered}$

Thus,

$\begin{gathered} 2x^2\rightarrow2x^2+15=h(x)\Rightarrow\text{ 15 units up} \\ \end{gathered}$

Hence, the answer is option C. Vertical stretch by a factor of 2 and a vertical shift by 15 units up.