Precal Blog

Today in honors Pre-Calculus hour 3, we discussed exponential functions. First we stated the basic equation for exponential functions can be written as f(x)= a*b^x. We further determined that exponential functions have certain “rules” they must follow, they are b>0, b can’t equal 1, and a can’t equal 0. For the first rule, if we use a number less than 0, like -2, our answers for the f(x) value would alternate from positive to negative. For the second rule, if b equals 1, we would simply get back the a value leaving us with a straight line. For the final rule, if a is equal to 0, our answer is 0 giving us nothing. With these rules in mind we looked at four different exponential graphs. I don’t have images so I’m sorry you must bear with my descriptions. The first graph was a>0, b>1. The graph was a positive exponential graph starting above the x-axis getting larger. The second graph was a<0, b>1. The graph was negative starting below the x-axis and sloping down into the fourth quadrant. The third graph was a>0, 0

Next we went over the 2.1 packet problem 3. We decided the domain for an exponential graph could be all real numbers, but the range had some stipulations. If a is negative, y<0; if a is positive, y>0. After testing the f(-x)=f(x) and f(-x)=-f(x) equations for even and odd symmetry, we decided that exponential graphs fit neither so they have no symmetry. Next we deduced that exponential graphs can increase or decrease everywhere, across the entire domain. Finally we looked at the concavity of exponential graphs. graphs can either can be concave up (“u-shaped” so they hold water) or concave down (upside down “u” so they shed water). In the case of exponential graphs if a>0, the graph is concave up; if a<0, the graph is concave down.

The last concept we discussed was “end behavior”. I’m not entirely clear on this concept (Mr. B said he struggled with it in high school so I don’t feel that bad) but basically it evaluates towards what “number” the graph is going. In the case of graph one from above the x-values are “going towards” positive infinity; and the f(x) values are also “going towards” positive infinity. When analyzing end behavior though you must make two sets of…”it”. One for the positive side and one going towards the starting point. So we have our positive side, now we look at the side going towards our starting point. in this case of graph one we have our x-values going towards negative infinity, and f(x) values going towards zero. Sorry if that was confusing, math terminology is beyond me so that’s my best attempt. We finished class by getting page 89 of the packet and to work on those problems. The next scribe will be Jake.