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{{ printedBook.courseTrack.name }} {{ printedBook.name }} First we need to draw the graph of $f(x)=-x−2.$ Let's make a table of values.

$x$ | $-x−2$ | $f(x)$ |
---|---|---|

$-2$ | $-(-2)−2$ | $0$ |

$0$ | $-0−2$ | $2$ |

$2$ | $-2−2$ | $-4$ |

We will now draw the graph of $f(x)$ by plotting these points and connect them with a line.

Next we want to draw the graph of $g(x)=f(-x).$ Let's find an expression for $g(x).$$f(x)=-x−2$

SubstituteExpressionsSubstitute expressions

$f(-x)=-(-x)−2$

NegNeg$-(-a)=a$

$f(-x)=x−2$

Substitute$f(-x)=g(x)$

$g(x)=x−2$

$x$ | $x−2$ | $g(x)$ |
---|---|---|

$-2$ | $-2−2$ | $-4$ |

$0$ | $0−2$ | $-2$ |

$2$ | $2−2$ | $0$ |

Let's now plot these points and connect them with a line.

The graph of $g(x)$ is a reflection of the graph of $f(x)$ in the y-axis. In the graph shown in the exercise, the reflection is done in the $x-$axis. This is the error.