The graph of the function $f ( x ) = x ^ { 2 } - 11 x + 7$ has been stretched horizontally by a factor of 2 . Find the function for the transformed graph.
A) $g ( x ) = \frac { x ^ { 2 } - 11 x + 7 } { 2 }$
B) $g ( x ) = 2 x ^ { 2 } - 22 x + 14$
C) $g ( x ) = \frac { x ^ { 2 } - 22 x + 28 } { 4 }$
D) $g ( x ) = 4 x ^ { 2 } - 22 x + 7$

Question

Quizplus · Accepted Answer

A horizontal stretch by a factor of 2 means replacing $x$ with $\frac{x}{2}$ in the function. So, $f(x) = x^2 - 11x + 7$ becomes $f\left(\frac{x}{2}\right) = \left(\frac{x}{2}\right)^2 - 11\left(\frac{x}{2}\right) + 7$, which simplifies to $\frac{x^2}{4} - \frac{11x}{2} + 7$. Multiplying through by 4 gives $x^2 - 22x + 28$, and dividing by 4 gives $\frac{x^2 - 22x + 28}{4}$.

The Graph of the Function f(x)=x2−11x+7f ( x ) = x ^ { 2 } - 11 x + 7f(x)=x2−11x+7

The Graph of the Function $f ( x ) = x ^ { 2 } - 11 x + 7$