This Student Problem goes over functions and explains how to graph one. As you can see, the function is composed of an exponent and is in the form of a parent graph. Using the values, key points, asymptotes, x-intercepts, y-intercepts, domain, range, and range, the image provided showcases a correct graph for the function. You will find that my ordered pair (2,-17) is off the graph, so it is place at the bottom of the graph just as a guide to help draw the graph.
In order to successfully solve this function, remember that there are some key factors that will determine the graph, such as the x-intercept. To find the x-intercept, start by substituting a 0 for the y-value and continue the process of solving the problem. After some addition (+5 to both sides) and diving (-3 to both sides), you will notice that you get -5/3. Move the exponent (x-1) to make it a coefficient and you will go over natural logs to get rid of the 4. However, the problem is that you cannot divide the logs, as LN -5/3 is negative and one cannot divide negative logs; it would be undefined, so there is no x-intercept. Remember that for the y-intercept, you have to solve the 4^-1 properly by finding its reciprocal of (1/4). For guidance, the "a" value will help you determine whether the asymptote is below or above, but in this case, it's above. For the key points, it's helpful to use ordered pairs that are not all so close together, so you can get a better view of your graph.
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