Suppose I'm graphing a graph like j(x) = -2 sin 4x. How can I tell if the origin is an x-intercept for it?
the origin is an x-intercept if f(0) = 0.
Is that true here?
Yes, the origin is an x-intercept here.
So how can I find the y-intercept in a function such as y = -2 sin(x - (pi/2)). I want to know from where to begin graphing, from the minimum or maximum value.
hey, come on. The y-intercept is where x=0!
So, just plug it in
y(0) = -2 sin(0-pi/2) = -2(-1) = 2
getting x-intercepts can be hard. Getting the y-intercept is trivial! Don't forget your Algebra I now that you're in trig.
To determine if the origin is an x-intercept for the function j(x) = -2 sin 4x, we need to check if j(0) equals zero.
To find j(0), substitute x = 0 into the given function:
j(0) = -2 sin(4 * 0)
= -2 sin(0)
= -2 * 0
= 0
Since j(0) = 0, we can conclude that the origin (0, 0) is an x-intercept for the graph of j(x) = -2 sin 4x.
By substituting the value of x into the function and evaluating it, we can determine whether a given point is an x-intercept or not.