Step 1: Graph the Area (using Desmos): This confirms that we are dealing with a negative area under the x-axis. In other to get a positive value we have to put a negative sign in front of the integral: In other words, you’re taking the negative of the integral solution (a negativ...
To put this another way, every function in a family is a transformation of a parent function. For example, the function f(x) = 2x is the linear parent function vertically stretched by a factor of 2; Instead of the function passing through (1, 1) the graph passes through (2, 1): Co...
In the particular “experimental brief” given to some students attending lessons here, internal resistance was to be determined using a “homemade” resistor of approximately ##\;4 \Omega## for the load. Measurements of open circuit voltage, terminal (load) voltage, and current were to be ma...
The article encourages students to make active decisions rather than passive ones when incorporating ChatGPT into their learning process. I argue that students should explicitly define their relationship with ChatGPT in their learning process, align their usage with their goals and values, and ...
You recall from the graph that H is steadily decreasing and levels off at 1. While a increases with time. So H is going to have to depend on the RECIPROCAL ##\frac{1}{1.3a}## which decreases as a gets large. In fact it depends very strongly--it depends on the CUBE...
So by definition, nonlinear functions produce graphs that aren’t a straight line. Linear function (red) and two nonlinear functions: exponential (blue) and polynomial (green). Graph created with Desmos.com. Nonlinear Function vs. Linear Function: Steps In order to figure out if your function ...
This function is trying to get to its limit of -1 (red dashed line), even if it doesn’t quite get there. Generally speaking, a limit puts some kind of boundary in place: a point where you can’t (or shouldn’t) go any further. For example, a maximum speed limit of 75 m.p....
If you were to plot the points above you would see that we end up with a “V” shaped plotted line identical to the absolute value parent function above, albeit with thevertexlocated at (-2, 0). Graph of y = |x + 2| Notice also that you could have used any values for x, provi...
This graph is a function because it passes the vertical line test. Properties of Functions All functions have certain properties, or distinct features, which can be very useful when trying to analyze them. The following common properties of functions describe how a graph is shaped, what happens ...
Step 6:Check your work. You could use a graphing calculator: I used the one atDesmos.comto create the graphs here. If you can’t use a graphing calculator, throw in a random x-value as an input, like x = 9.2 or x = 7.5. If you have drawn your graph correctly, your new point...