Graph f(x)= second(2x+3.14/4)
You do need help.
secant is not second.
why don't you graph the cosine curve, then sketch the reciprocal (secant).
To graph the function f(x) = second(2x + 3.14/4), we first need to understand what the "second" function represents.
The term "second" typically refers to the secant function, which is the reciprocal of the cosine function. The general form of the secant function is sec(x) = 1/cos(x). However, in your case, the "second" function appears to be applied to an expression inside the parentheses.
To graph the function f(x), we will follow these steps:
Step 1: Identify the phase shift
The expression inside the parentheses, 2x + 3.14/4, determines the phase shift of the function. To find the phase shift, set 2x + 3.14/4 = 0 and solve for x. In this case, 2x = -3.14/4, which gives x = -3.14/8. This means the graph will be shifted horizontally by -3.14/8 units.
Step 2: Determine the period
The period of the secant function is 2π. Since there are no additional coefficients or constants affecting the x-term, the period remains unchanged.
Step 3: Find the vertical asymptotes
The secant function has vertical asymptotes at x-values where the cosine function has zeros. Since the cosine function has zeros at x = (2n + 1)π/2, where n is an integer, the secant function will have vertical asymptotes at x = (2n + 1)π/2.
Step 4: Plot key points
Choose several key values for x within an interval of one period, such as x = -π/4, 0, π/4, π/2, π, etc. Evaluate f(x) = second(2x + 3.14/4) at these x-values to get corresponding y-values.
Step 5: Sketch the graph
Using the phase shift, period, vertical asymptotes, and the key points obtained in Step 4, sketch the graph of f(x) = second(2x + 3.14/4).
Note: Since the secant function is unbounded, the graph may stretch to infinity or negative infinity at certain points.