Graph f(x) = 4^x and g(x) = log4 x in the same rectangular coordi...

Question

Graph f(x) = 4^x and g(x) = log4 x in the same rectangular coordinate system.

Accepted Answer

Hey, everyone here we are asked to graph the following equations. F of X is equal to two to the power of X and G of X is equal to log base two of X. Here we have four answer choice options. ABC and D each with a different graph containing the functions F of X and G of X. To begin solving this problem, we can first consider our first given function F of X. And if we recall, we know that we have F of X is equal to two to the power of X. And so to start graphing this function, we first need to start by considering various X values. So we can get ordered pairs. So we can begin by substituting in negative four for X into our function. So we have F of negative four is equal to two to the power of negative four. And now simplifying we get 1/16 which in decimal form is 0.625. Then so now we just want to repeat this process with multiple other X values and set up a table of values. So for our table of values, we have our X and Y values. And so we can choose any X values really. But here we will have negative four, negative three, negative two, negative 10 and one. And then substituting in all of these X values into our function, we get our Y values. So we have 0.625, then 0.1250 point 250.51 and two. So now with our table of values, we can go ahead and plot of these ordered pairs in a graph. And so doing this, we have our various points plotted on our graph here. And so the next step after plotting these points is to simply connect points with a smooth line. So we form our graph of F of X. So this smooth line here we see approaches the X axis but never crosses it. And again, this smooth line is our function F of X. So now that we have graphed our first given function F of X, we can move on to working to graph our second function which is G FX is equal to log base two of X. And so now we want to repeat a similar process. But here we need to notice that the logarithmic function is defined only for when X is greater than zero. So the values for X that we will consider will only be those that are greater than zero. So we can begin by substituting in X is equal to one into the equation. So we have G of one is equal to log base two of one. And now simplifying we just get zero. So again, we want to repeat this process to get our table of values here. So our values for X that we are going to choose here are just 123 and four. And now we want to just substitute in each of these X values into our G FX function to get our Y values and we get 11.58 and two. And now with these X and Y values, we can plot these points on a graph. And so plotting these points, we see we have our four points on our graph. And then the next step just like before is to connect these points with a smooth line. In connecting these points. We see we get our function 4G of X. So again, this smooth line here is our function G FX graph. So now we see we have graphed our two functions F of X and G of X individually. So the next step is to just combine the two graphs. So we have both the functions on one coordinate system. So here we see our final graph where the top line is our F of X function and then the lower line is the G of X function. So now with this final graph, we see here that our final answer we are left with answer choice. C Thanks for watching. I hope you found this video helpful and I'll see you again next time.

Graph f(x) = 4^x and g(x) = log4 x in the same rectangular coordinate system.

Key Concepts

Exponential Functions

Logarithmic Functions

Graphing Functions

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