Graph each function. ƒ(x) = log￬1/2 (x+3) - 2

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Accepted Answer

Graph the following logarithmic function where we have F of X equals log base 1/4 X plus five minus four. Now, to graph this, we're gonna make the table input and output values you have X and our function F of X. Now we know this, we actually shifted on our graph. We have an X plus five inside of our log function, which means we are shifted five units to the left. Russell shifted down by four. Now to find some input values, you notice, since we're shifted to the left, we can start, let's say at negative five with log functions, the number inside of our function has to stay positive. If it's zero or negative, we will get unde fact. So for instance, if we use X equals negative five, we plug in negative five, we will get luck based on fourths with negative five plus five minus four, which gives us the log of zero minus four, which in that case is undefined. So we need values greater than negative five plus. They would choose maybe 4.5, native four, negative three, negative two and negative one. We can plug each of these into our function 4.5. 1st gives us lug base 1/4 negative 4.5 plus five minus four. We have to simplify this. We get 4.5, you plugged in negative four. We would give four, three, we only get 3.5 two. We would get about 3.21. And for one, we would get three, we cannot plot every one of these points on our graph. Now, because negative five is un defined. We have an as to at X equals negative five. But we can plot the rest of our points negative 4.5 and up 4.5, negative four, up four, negative 3, 3.5, negative 23.2 and negative one, positive three. Now this is a log function as soon as we need the draw line following our Asymptote through all of our points. So we start from the top, draw the line, go through our points and we continue flattening out to the right. All right. So this is how the graph of this function would look. I hope to help you solve the problem. Thank you for watching. Goodbye.

Graph each function. ƒ(x) = log￬1/2 (x+3) - 2

Key Concepts

Logarithmic Functions

Transformations of Functions

Domain and Range of Logarithmic Functions

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