Student Problem #3: Unit I Concept 1

• What is this problem about?
• This problem is an example problem from Unit I Concept 1. It is graphing exponential graphs. We are given an equation and in order to graph a good exponential graph we need a horizontal asymptote, an x-intercept, a y-intercept and key points.

• What must the reader pay close attention to in order not to make a mistake?
• The reader must remember a few important things. To begin with, your "k" is your asymptote. The "a" tells you if your graph will be below or above the asymptote depending is it is negative (below) or positive (above).  First, the Exponential YaK Died is an important phrase that helps us remember two things: in exponential graphs, y=k so our asymptote will be horizontal and the domain will have no restrictions, meaning it will be all real numbers. Also, the reader must pay attention to the range. It is dependent on where the asymptote lies. If the graph is negative and it lies below the asymptote, then the range will start with (-infinity, the asymptote value). Or if the graph is positive and it lies above the asymptote, then your range would look like (asymptote value, infinity). *we use parenthesis because 1) infinity........PARENTHESIS! and 2) the graph cannot touch the asymptote. And lastly, your "h" should be your third key point.