Question

what does the transformation ( f(x)\to2f(x) ) do to the graph of ( f(x) )?

stretches it horizontally

shrinks it vertically

stretches it vertically

shrinks it horizontally

Explanation:

For a function \( y = f(x) \), when we have a transformation \( y = af(x) \) (where \( a>1 \)), it is a vertical stretch. Here \( a = 2>1 \). A vertical stretch means that for each \( x\)-value, the \( y\)-value of the function is multiplied by \( 2 \). So the graph of \( y = 2f(x) \) is a vertical stretch of the graph of \( y=f(x) \). Horizontal stretches/shrinks are of the form \( y = f(bx)\) where \( b
eq1 \). Vertical shrinks are of the form \( y=cf(x)\) where \( 0 < c<1 \).

Answer:

stretches it vertically