In Exercises 53-58, begin by graphing f(x) = log₂ x. Then use tra...

Question

In Exercises 53-58, begin by graphing f(x) = log₂ x. Then use transformations of this graph to graph the given function. What is the vertical asymptote? Use the graphs to determine each function's domain and range. g(x) = (1/2)log₂ x

Accepted Answer

Graph. The following function by graphing first, its parent function F of X equals to log X and performing transformation determined as vertical ascent to domain and range. Our function we want is GMX equals 1/4 log X. We have four graphs here as possible answers. Now, so this, we need to first find is transformation. So we have F of X is YX and G FX is 1/4 log X to find our points, we can make use of a table CMF of X and G FX. And we'll say X equals one and X equals four. So for F FX, we plug in one to get log of one log of one is zero for four. We want log of four which we plug into a calculator is about 0.6. For G FX, we would say GF one which our case is still gonna be zero for X equals four, we would have 1/4 multiplied by log of four. Now we said log of four was 0.6. So 1/4 of log four would be 0.15. We now need a graph that has two points, 10 and 4. 0.15 we can also determine the vertical Asymptote domain and range. Since our transformation is just a vertical shrink, we do not have any movement to the left, right up or down. So our domain arrange should be the same as our F FX, the domain or log X will then be any value squarer than zero. In other words, the interval zero to infinity. Similarly, for the wrench, we go down to negative infinity and up to positive affinity. So we have negative infinity to infinity. A vertical ascent to then will be very similar to our domain and that we cannot pass the value X equals zero. So in other words, our vertical Asymptote is X equals zero. We now have all of the information we need. We have our domain a range and I wear a glass and to, and we have our points of our new graph. This makes sense to our problem answer B OK. I hope to help you solve the problem. Thank you for watching. Goodbye.

In Exercises 53-58, begin by graphing f(x) = log₂ x. Then use transformations of this graph to graph the given function. What is the vertical asymptote? Use the graphs to determine each function's domain and range. g(x) = (1/2)log₂ x

Key Concepts

Logarithmic Functions

Transformations of Functions

Asymptotes, Domain, and Range

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