because everything relies on the basic axioms, and all arguments should derive from it. However, in most cases you don't need to prove a self-evident claim like this. It's useful, but not necessary to understand the formal reasoning of a proof of something really simple, so ...
How do you graph absolute values of curvy lines?To graph a function that contains the absolute value of a curvy line (such as a cubic polynomial), follow these steps:Find the x-intercepts of the curvy line inside the absolute-value bars. These points are where the graph will turn back ...
{/eq}. The graph of an inverse function is the reflection of the graph of the original function about the line {eq}y = x {/eq}.One-to-one functionshave inverses. One-to-one functions pass thehorizontal line test: any horizontal line drawn through the graph of the functio...
know the x coordinate is 17.5, but I don’t know the y coordinate. Is there a way I could plot the x coordinate on the polynomial and use the information from the graph to figure out the y coordinate? This coordinate needs to be distinguished from the points (e...
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In mathematics, graphs provide visual representations of problems to promote understanding. Discover the steps to solve and graph 1 - cos(x) and...
I have a set of data and I want to compare which line describes it best (polynomials of different orders, exponential or logarithmic). I use Python and Numpy and for polynomial fitting there is a function polyfit(). But I found no such functions for exponential and logarit...
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Just because all of the examples so far have involved polynomial functions, don't think that the concept of even and odd functions is restricted to polynomials. It's not. Trigonometry is full of functions that are even or odd, and other types of functions can come under consideration, too....
The same process works for solving and graphing the solution set of an inequality. Consider that you're asked to solve and graph the inequality -y ≥ 2x You'll follow almost exactly the same steps as solving an equation, with a couple of quirks introduced by the presence of the inequality...