Question

looking at the parent function of $f(x)=|x|$, how would the graph of $t(x)=-f(x)$ be different? graph using the drawing tools.

Explanation:

Step1: Define transformed function

$t(x) = -f(x) = -|x|$

Step2: Identify reflection rule

Multiplying a function by $-1$ reflects its graph across the $x$-axis.

Step3: Map key points of parent

Parent $f(x)=|x|$ has points: $(0,0)$, $(1,1)$, $(-1,1)$, $(2,2)$, $(-2,2)$

Step4: Reflect points over x-axis

Reflected points: $(0,0)$, $(1,-1)$, $(-1,-1)$, $(2,-2)$, $(-2,-2)$

Step5: Draw transformed graph

Connect reflected points to form the V-shaped graph opening downward.

Answer:

The graph of $t(x) = -f(x)$ is the reflection of $f(x)=|x|$ across the $x$-axis, forming a V-shape that opens downward with its vertex at $(0,0)$. Key points include $(1,-1)$, $(-1,-1)$, $(2,-2)$, $(-2,-2)$.