THIS USER ASKED 👇
Which functions are symmetric with respect to the y-axis? check all that apply. a. f(x) = |x| b. f(x) = |x| + 3 c. f(x) = |x + 3| d. f(x) = |x| + 6 e. f(x) = |x – 6| f. f(x) = |x + 3| – 6
THIS IS THE BEST ANSWER 👇
Answer: A, B and D.
We need to find the functions that are symmetrical about the y-axis
A. f (x) = | x | it is always symmetrical about the y axis because the vertex is at the base and we get a V – shape graph.
B. f (x) = | x | +3 is symmetrical about y-axis. We know f (x) = | x | it is always symmetrical about the y axis. 3 is added at the end so that the graph is translated. So the symmetric graph is still about y y.
C. f (x) = | x + 3 | it is not symmetrical about the y axis because 3 is added to x so we move the graph f (x) = | x | three units left.
D. f (x) = | x | +6 is symmetric under y-axis. f (x) = | x | it is always symmetrical about the y axis. 6 is added at the end so that the graph is translated. So the symmetric graph is still about y y.
E. f (x) = | x – 6 | it is not symmetric about the y axis because 6 is subtracted by x so we make a graph of f (x) = | x | six units on the right.
F. f (x) = | x + 3 | – 6 is not symmetrical under y-axis. 3 is added to x and 6 is subtracted at the end. so we move the graph f (x) = | x | 6 units down and 3 units left. So the graph is not symmetric under y-axis.
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