Graph each function. Give the domain and range. ƒ(x) = | log￬2 (x...

Question

Graph each function. Give the domain and range. ƒ(x) = | log￬2 (x+3) |

Accepted Answer

Consider the logarithmic function F of X equals the opposite value of log base six X plus five graph and identify its domain and range. Now to graph this, I'm just gonna find a few points to plot on the graph. So make a table X and F of X. Now for lux the inside of the log function cannot be a negative value. Otherwise we get an undefined, it also cannot be equal to zero. Let's set the inside power of our log function equals to zero. We get X equals negative five. That means any value less than negative five will be undefined. So add that to the table. Let's find a few other values for our graph negative 4.5, negative four, negative three, negative two and negative one. All work. Let's go ahead and plug these into our function F negative five we mentioned before was on the five because it makes a log have a zero in set. Let's plug in negative 4.5. We plugged in negative 4.5. We get an approximation of about positive 0. type in negative four. We would get zero for three, we get 0.39 two, we get 0.61. And finally, for one, we get 0.77, we now have a few points. We can plot onto our graph. Let's say our first one happens at negative four point a half 0.39. And we can mark on a graph here. That point is roughly about there. We have negative 40, negative 30.39 negative 20.61 and N of 10. which now draw a graph. Now we know we cannot go past negative five to the left which means we have an as tode this graph then will start from infinity. Go down touch the X axis and then continue going on to the right. We cannot find our domain remains since we cannot go less the negative five, our domain will be from negative five to infinity. Our range is all possible Y values and we notice we do not go anywhere lower, then Y equals zero. So our range will be from zero. So we go up to infinity because we have an arrow pointing upwards. OK? I hope to help you solve the problem. Thank you for watching. Goodbye.

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Graph each function. Give the domain and range. ƒ(x) = | log￬2 (x+3) |