Question

the table represents the linear function $f(x)$.

$x$	$-3$	$-2$	$-1$	$0$
$f(x)$	$-25$	$-19$	$-13$	$-7$

if $g(x) = 11f(x)$, identify the transformation performed on $f(x)$.
vertical compression
vertical stretch
horizontal compression
horizontal stretch

Explanation:

To determine the transformation from \( f(x) \) to \( g(x) = 11f(x) \), we recall the rules of function transformations. For a function \( y = a \cdot f(x) \), if \( |a|>1 \), it is a vertical stretch (the graph is stretched vertically by a factor of \( |a| \)). Here, \( a = 11 \), and \( |11|>1 \), so it is a vertical stretch. Horizontal transformations involve changes to the input \( x \) (e.g., \( f(bx) \)), while vertical transformations involve changes to the output \( f(x) \) (e.g., \( a \cdot f(x) \)). Since \( g(x) \) multiplies the output of \( f(x) \) by 11, it is a vertical transformation, and because \( 11>1 \), it is a vertical stretch.

Answer:

Vertical stretch