Question

The graph of
f
(
x
)
=
x
2
−
2
x
−
3
is shown.



image.png



Which of these describes the effect changing
f
(
x
)
to
f
(
−
2
x
)
will have on the graph?


The graph will translate down 2 units.


The graph will change from opening up to opening down.


The graph will stretch horizontally.


The graph will shrink horizontally.

Answer 1

The graph will shrink horizontally.

Reason: f(-2x) = f(kx) with k = -2 causes a horizontal scaling by factor 1/|k| = 1/2 (a horizontal shrink to half the width); the negative also reflects across the y‑axis.