Reflections of Graphs Flashcards

All 6 cards in this deck

What transformation maps the graph of $y=f(x)$ onto the graph of $y=-f(x)$?

A reflection in the $x$-axis.
Each point $(p,q)$ maps to $(p,-q)$.

What transformation maps the graph of $y=f(x)$ onto the graph of $y=f(-x)$?

A reflection in the $y$-axis.
Each point $(p,q)$ maps to $(-p,q)$.

True or false? The graph of $y=f(-x)$ is the graph of $y=f(x)$ reflected in the $x$-axis.

False. It is a reflection in the $y$-axis; $y=-f(x)$ is the reflection in the $x$-axis.

The point $(7,2)$ lies on the curve $y=f(x)$. What are the coordinates of the corresponding point on the curve $y=f(-x)-3$?

$(-7,-1)$.
Reflection in the $y$-axis, then a translation 3 units down.

Graph A has equation $y=g(x)$. Graph B is the reflection of graph A in the $y$-axis. Write down an equation of graph B.

$y=g(-x)$.

The graph of $y=\sin x^\circ$ is reflected in the $x$-axis. Write down an equation of the reflected graph.

$y=-\sin x^\circ$ (or equivalently $y=\sin(-x)^\circ$).