Question

question 1 - 11
which of the following shows the absolute value function ( g(x)=|x - 2|+3)?

Explanation:

Step1: Identify vertex of absolute function

The vertex form of an absolute value function is $y = a|x-h|+k$, where $(h,k)$ is the vertex. For $y(x)=4|x-2|+3$, the vertex is $(2, 3)$.

Step2: Check slope and direction

For $x>2$, $y=4(x-2)+3=4x-5$, slope $=4$ (steep positive). For $x<2$, $y=4(2-x)+3=-4x+11$, slope $=-4$ (steep negative).

Step3: Match to graph options

Find the graph with vertex at $(2,3)$, steep positive/negative slopes, and $y$-intercept at $y=4|0-2|+3=11$ (when $x=0$). The top-most graph matches these properties.

Answer:

The top graph (first option) is the correct graph for $y(x)=4|x-2|+3$.