horizontal shift. The cosine function, which appears to have a "head start" on the sine function, is often said toleadthe sine function (or the sine functionlagsthe cosine function). Both sine and cosine fall under the category of sinusoids, since the cosine graph is simply a 90º shift...
But, instead of shifting the graphed sine wave three units up, I'll add room underneath my current graph, shift the horizontal axis three units down, and then re-number the y-axis: The above is the same graph as the first one I did, but all I've really done is moved the x-axis...
In summary, the conversation discusses finding invariant points between a base trigonometric function and a horizontally stretched function. The only invariant point for a horizontal stretch is when x = 0, as all other points on the graph are affected by the transformation. ...
A line with a slope of zero is horizontal as in (Figure)(c). Figure 5. Increasing and Decreasing Functions The slope determines if the function is an increasing linear function, a decreasing linear function, or a constant function. f(x)=mx+bf(x)=mx+bis an increasing function ifm>0.m...
The equationf(x)=bx+df(x)=bx+drepresents a vertical shift of the parent functionf(x)=bx.f(x)=bx. The equationf(x)=bx+cf(x)=bx+crepresents a horizontal shift of the parent functionf(x)=bx.f(x)=bx.See (Figure). Approximate solutions of the equationf(x)=bx+c+df(x)=bx+c...