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

Considered a logarithmic function F of X equals log base seven X plus six graph and identify its domain in range to graph this. Let's first make a table of values now because this is a log function and we're not shifting to the left or to the right. Our X cannot be a negative value and it also can't be zero. I'll put a zero here just to show what happens. But we have zero and then we have a few other points after. So we have one half, 123 and four. Let's plug in all of our values. If we plug in zero, we can't log up to zero. Now log of zero is undefined. This means log zero will leave as an fact overall for one half, we get logged base 71 half plus six. That value approximates to 5.64. Let's plug in more values. We plugged in one, we will get six, two, we would get 6.36 3, we would get 6.56 and finally four, we would get 6.71. Let's try plugging in or plotting all of these to the graph. So our first point is one half 5.64, you'll plot that. And about there, we have 16, next 26. 36.56 and 46.71. Now this is a log function. So this function will drop all the way down to negative infinity as it approaches our as to the left as it approaches zero, we're going down to eight infinity, we curve up through our points and then we keep going to the right now. We can find our domain in range. Our domain is all of our possible X values. Now, we can't be equal to zero because it's undefined, which means we will have zero to infinity with rounded brackets for the range. We can go all the way down to negative vicinity and we go up to positive infinity as we go to the right. That means our range goes from negative infinity to infinity. We now have our graph and our domain and ranch. OK. I hope to help you solve the problem. Thank you for watching. Goodbye.

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

Key Concepts

Logarithmic Functions

Domain and Range

Graphing Functions

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