which of the following is the graph of this absolute value function? y = |x| + 2
which of the following is the graph of this absolute value function? y = |x| + 2
Answer
Explanation:
Step1: Recall the parent absolute value function
The parent absolute value function is ( y = |x| ), which has its vertex at ( (0, 0) ) and opens upwards (a V - shape).
Step2: Analyze the transformation
For the function ( y=|x| + 2 ), we are adding 2 to the parent function ( y = |x| ). In the transformation of functions, if we have a function ( y = f(x)+k ), when ( k>0 ), the graph of ( y = f(x) ) is shifted up by ( k ) units. Here, ( f(x)=|x| ) and ( k = 2 ), so the graph of ( y=|x| ) is shifted up by 2 units. This means the vertex of the graph of ( y=|x| + 2 ) will be at ( (0, 2) ).
Step3: Analyze the options
- The first graph has its vertex at ( (- 2,0) ), which is a horizontal shift, not a vertical shift of the parent function. So it is not the graph of ( y = |x|+2 ).
- The second graph has its vertex at ( (0, 2) ) and has the characteristic V - shape of an absolute value function, shifted up by 2 units from the parent function ( y = |x| ).
- The third graph has its vertex at ( (0,-2) ), which is a vertical shift down by 2 units, not up. So it is not the graph of ( y=|x| + 2 ).