which functions could be represented by the graph? check all that apply. f(x)=|x + 0.14| f(x)=|x|+1.3…

which functions could be represented by the graph? check all that apply. f(x)=|x + 0.14| f(x)=|x|+1.3 f(x)=|x - 7| f(x)=|x + 12| f(x)=|x|-17 f(x)=|x - 23|

which functions could be represented by the graph? check all that apply. f(x)=|x + 0.14| f(x)=|x|+1.3 f(x)=|x - 7| f(x)=|x + 12| f(x)=|x|-17 f(x)=|x - 23|

Answer

Explanation:

Step1: Recall properties of absolute - value functions

The general form of an absolute - value function is $y = a|x - h|+k$, and its vertex is at the point $(h,k)$. For the basic absolute - value function $y = |x|$, the vertex is at $(0,0)$. A function of the form $y=|x - h|$ has a vertex at $(h,0)$ and $y = |x|+k$ has a vertex at $(0,k)$.

Step2: Analyze the vertex of the given graph

The vertex of the given graph is at the origin $(0,0)$.

Step3: Check each function for the vertex

  • For $f(x)=|x + 0.14|$, the vertex is at $(- 0.14,0)$.
  • For $f(x)=|x| + 1.3$, the vertex is at $(0,1.3)$.
  • For $f(x)=|x - 7|$, the vertex is at $(7,0)$.
  • For $f(x)=|x + 12|$, the vertex is at $(-12,0)$.
  • For $f(x)=|x|-17$, the vertex is at $(0, - 17)$.
  • For $f(x)=|x|$, the vertex is at $(0,0)$.

Answer:

No options provided exactly match the graph. If we assume the basic $y = |x|$ was an option (not listed here but based on vertex analysis, a function with vertex at $(0,0)$ is needed), a correct - form function would be of the form $f(x)=|x|$ with no horizontal or vertical shifts. If we consider the closest in the given list in terms of general form, none of them are correct as they all have non - zero horizontal or vertical shifts.