Question

what does the transformation ( f(x)\to2f(x) ) do to the graph of ( f(x) )?
shrinks it horizontally
stretches it vertically
stretches it horizontally
shrinks it vertically

Explanation:

When we have a transformation of the form \(y = af(x)\) where \(a> 1\) (in this case \(a = 2\)), for each \(x\) - value, the \(y\) - value of the function is multiplied by \(a\). This means that if we consider a point \((x,y)\) on the graph of \(y=f(x)\), the corresponding point on the graph of \(y = 2f(x)\) is \((x,2y)\). Since the \(y\) - values (vertical direction) are being multiplied by a factor greater than \(1\), the graph is stretched vertically. Horizontal transformations would involve changes inside the function, such as \(f(bx)\) where \(b
eq1\). Shrinking vertically would occur if \(0 < a<1\).

Answer:

stretches it vertically