Student Problem #3: Unit I Concept 1

• What is this about?

This picture shows a problem from Unit I Concept 1 which is graphing exponential functions and identifying x-intercept, y-intercept, asymptotes, domain, range (4 points on graph minimum). It is about graphing exponential graph by using the given equation. It is involved with a (POSITIVE- above the x-axis, NEGATIVE- below the x-axis), b (abs. of b > 1: close to the asymptote on the left side, abs. of b < 1: close to the asymptote on the right side), h (shifts the graph left or right), k (horizontal asymptote, y = k). We will use the graphing calculator to make the graph more accurate by finding the key points. Also, we will write the correct limit notations for domain and range. The graph requires at least more than 4 points. 

•  What does the reader need to pay attention to?

The reader needs to pay attention when he or she looks for x-intercept. In this case, there is no x-intercept. You can know it by looking at the graph, the asymptote is -3 and the graph stays below the x-axis which means the graph cannot touch the x-axis. When the reader looks at the calculation for x-intercept. We CANNOT log a negative number that makes it undefined. But the actually way to put as the answer is "No x-intercept". For the limit notation of the range, we will have it written from bottom to top so the negative inf. to the positive inf. But when the asymptote is there, in this problem, the range will be (-inf., -3) and -3 is the asymptote.