Symmetry: Identify the symmetry in the graphs of the following equations. ? a. ?y = cos 3?x ? ? b. v? =? 3x? 4 ? 3x ? 2 + 1 ? ? c. v? 2 ? 4x ? 2 = 4

Step-by-step solution Step 1 To find the symmetry of the given functions, we use the following test: If a function f satisfies f(x) = f(x) for every number x in its domain, then f is called an even function. Even functions are symmetric about the y-axis. If a function f satisfies f(x) =f(x) for every number x in its domain, then f is called an odd function. Odd functions are symmetric about the origin. Step 2 a) We need to identify the symmetry in the graph of y = cos 3x . Step 3 To find the symmetry of the graph of y = cos 3x , we identify if the function is odd or even. First, we check if y = cos 3x is even. For this, we let x = . cos (3x) = cos 3x cos (3) = cos 3 1 =1 f(x) = f(x)even Since y = cos 3x , we know that the function is symmetric about the y-axis. Step 4 Next, we check the symmetry of the graph of y = cos 3x by graphing: Step 5 Based on the symmetry test and the graph of y = cos 3x , we know that the function is symmetric about the y-axis. Step 6 b) We need to identify the symmetry in the graph of v = 3x 3x +1. 2 Step 7 To find the symmetry of the graph of v = 3x 3x +1, we identify if the function is odd or even. First, we check if v = 3x 3x +1 is even. For this, we let x = 1. 4 2 4 2 3(x) 3(x) +1 = 3x 3x +1 3(1) 3(1) +1 = 3(1) 3(1) +1 2 1 = 1 f(x) = f(x)even Since v = 3x 3x +1, we know that the function is symmetric about the y-axis.