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. Here that's shown on our diagram. Below graph the area of function A X equals the integral of F of T with respect to T between the limits of 0 and X on or blank graph. Now, if we're going to graph the area of function, and we know it's the integral of FFT, let's go back to FFT and ask ourselves, what do we know about this function. Well, we recognize that the graph of FFT is a concave or parabola below the T-axis, OK? So since F of T is below the T-axis from T equals 0 to T equals A, then that means. OK, that the area function, which is the integral of FFT with respect to T, is going to be decreasing. So that's the first thing FFT tells us about our area function AF X. Also, we noticed that the graph of FFT is concave up. So F of X is increasing, OK, which means then that A of X is going to be concave up, OK. Therefore, the area function is decreasing. And it's concave up on the interval from 0 to a. No, we can use that to help us plot A of X because now by comparing that tells us the slope of a of X is going to be steepest at the X coordinate of the vertex of the parabola, OK. It's gonna be somewhere here. And toward the end of the interval, the graph continues to decrease but becomes less steep. So A of X is going to look something like this, OK? This is the graph of Y equals A X. Thanks a lot for watching everyone. I hope this video helps.

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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