which functions have a vertex with a x - value of 0? select three options.\n□f(x)=|x|\n□f(x)=|x| +…
which functions have a vertex with a x - value of 0? select three options.\n□f(x)=|x|\n□f(x)=|x| + 3\n□f(x)=|x + 3|\n□f(x)=|x| - 6\n□f(x)=|x + 3| - 6
Answer
Explanation:
Step1: Recall vertex - form of absolute - value function
The general form of an absolute - value function is (y = a|x - h|+k), and its vertex is ((h,k)).
Step2: Analyze (f(x)=|x|)
For (f(x)=|x|), we can write it as (f(x)=1|x - 0|+0). The vertex is ((0,0)), so the (x) - value of the vertex is (0).
Step3: Analyze (f(x)=|x| + 3)
For (f(x)=|x|+3), we can write it as (f(x)=1|x - 0|+3). The vertex is ((0,3)), so the (x) - value of the vertex is (0).
Step4: Analyze (f(x)=|x + 3|)
For (f(x)=|x + 3|), we can write it as (f(x)=1|x-(-3)|+0). The vertex is ((-3,0)), so the (x) - value of the vertex is (-3\neq0).
Step5: Analyze (f(x)=|x|-6)
For (f(x)=|x|-6), we can write it as (f(x)=1|x - 0|-6). The vertex is ((0,-6)), so the (x) - value of the vertex is (0).
Step6: Analyze (f(x)=|x + 3|-6)
For (f(x)=|x + 3|-6), we can write it as (f(x)=1|x-(-3)|-6). The vertex is ((-3,-6)), so the (x) - value of the vertex is (-3\neq0).
Answer:
(f(x)=|x|), (f(x)=|x| + 3), (f(x)=|x|-6)