3. Representa cada función en el plano cartesiano. Luego,...

3. Representa cada función en el plano cartesiano. Luego, indica si es una función creciente o decreciente. a. f(x) = 4? | x | -3 | -2 | -1 | 0 | 0,5 | 1 | 1,6 | | :--- | :--- | :--- | :--- | :--- | :--- | :--- | :--- | | f(x) | | | | | | | | Función: b. g(x) = e?? | x | -3 | -2 | -1 | 0 | 0,5 | 1 | 1,6 | | :--- | :--- | :--- | :--- | :--- | :--- | :--- | :--- | | g(x) | | | | | | | | Función:

Transcript

00:01 Let's start by filling out the table.

00:04 Okay, so we'll find f evaluated at negative three.

00:09 This is four to the negative third power, which is approximately 0 .02.

00:22 So we have zero comma zero two.

00:27 So when we plot that, we are at negative three and just barely above negative three.

00:35 Okay, now let's go to the next value, f evaluated at negative two.

00:40 So that's four to the negative second power, which is about zero comma zero six.

00:48 Okay, so when we plot that, we have negative two and almost at one.

00:57 So about here.

01:04 I'm sorry, i meant almost at zero comma one.

01:07 Okay, so that's closer to this point here.

01:12 Okay, let's go to the next point, f evaluated at negative one is four to the negative first power.

01:22 This is just one fourth, which is 0 .25.

01:27 Okay, so when we plot this, we have negative one and we're exactly at this intersection here.

01:36 Okay, next point, f of zero is four to the zeroth power, which is one.

01:45 Okay, so we have the point zero one, f of zero comma five is four to the zero comma five power, which is four to the one half power.

02:02 So that's the square root of four, okay, which is two.

02:08 So this is two.

02:10 So we'll plot it as one half and two.

02:18 Okay, then f of one is four to the first power, which is just four.

02:24 Okay, so we have the points one, four.

02:27 And finally, f of one comma six is four to the one comma six power, which is approximately 9 .2.

02:41 Okay, so we have nine comma two.

02:47 Okay, so that value is off the charts.

02:50 It would be somewhere around here.

02:54 Okay, so now let's connect the points.

02:59 Okay, so this is the representation in the cartesian plane.

03:03 I see that the slope is positive, which means that the function is increasing.

03:10 Another way to check if the function is increasing or decreasing is by taking the first derivative of the function.

03:18 Okay, so the first derivative is equal to four to the x power times the natural log of four.

03:28 And four to the x power is always positive.

03:31 And natural log of four is positive.

03:34 And a positive times a positive is positive.

03:37 Okay, so that means that the first derivative is always positive...

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