Matching functions with area functions Match ...

Question

Matching functions with area functions Match the functions ƒ, whose graphs are given in a― d, with the area functions A (𝓍) = ∫₀ˣ ƒ(t) dt, whose graphs are given in A–D.

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Accepted Answer

Welcome back everyone. Consider the graph of FFT as shown in our diagram. Graph the area function A X equals the integral of F of T with respect to T between 0 and X and the blank graph that follows. Now, if we're going to graph the error function FFX, first we notice that it's the integral of FFT. What do we know about the function FFT? Well, by looking at FFT, we notice, OK, we can tell that FFT, OK. On the interval from 0 to 8 is a horizontal line. Horizontal line. Below the t axis. Now what do we know about the equations of horizontal lines? Well, we know that it's going to be a constant, so we can let F of T be equal to negative K, OK, where K is going to be positive. So now we know that about FFT to find AFX we can integrate FFT with respect to T. In other words, this means that AFX, actually, let me put that in blue. A of X Is going to be equal to the integral between 0 and X of negative K with respect to T. When we integrate negative K, it equals negative K T. That's between the bounds of 0 and X are in the interval from 0 to X, which is going to give us negative k X. Thus, A X or error function equals negative KX. Now, if we think about it, this is in the form of a linear equation. It's a linear function. So that means A X is going to be a straight line on the interval from 0 to a with a negative slope of negative K, OK, because this, the coefficient of X, represents the slope of our line. So that means we can go back to our graph and draw our line negative KX and that is going to be our function Y equals A X. Thanks a lot for watching everyone. I hope this video helped.

Matching functions with area functions Match the functions ƒ, whose graphs are given in a― d, with the area functions A (𝓍) = ∫₀ˣ ƒ(t) dt, whose graphs are given in A–D.

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