Blog 29: Investigation y = b^x

imageLots of things apply when it comes to the equation y=b^x. Like how the y-intercept is always 1, negative numbers do not work, and there may be an asymptote. Changing the value of b will change the slope of the line. The greater b is, the steeper the graph. For example, you can see in the picture that when b=7 it is steeper than the other two. The picture doesn’t show but, none of the equations pass the x-intercept because of the asymptote.

 

Blog 30: Multiple Representations Web for Exponential Functions

imageSo far in this lesson, we have had a few problems showing how to turn an equation to a table or graph, and a graph to explain a situation. Even though this is all we’ve been taught, I think it would be easy to map out the other parts of the web. In my opinion one thing that might be difficult would be figuring out an equation from the graph. Examples from the lesson showing my learning were problems 8-21, 8-22, and 8-24.

 

Blog 31: Updated Web for Exponential Functions

imageThe only few things we were able to add the the web were the connections between the equations and tables or graphs. Even though we already knew how to find one with the other, this lesson helped us finding it the other way around. Like I said in the last web blog, although we didn’t find the other connections, it would be easy to solve either way.

 

 

Blog 32: Graph → Equation for Exponential Functions

imageWhen it comes to converting exponential graphs to equations, there are many simple steps. At first you take the y-intercept and plug it in as b in the equation y=b•m^x. To continue, you divide the y value of x=1 by the y-intercept, and for x=2, x=3, etc. From there you get the multiplier then plug it in as m in the equation.

 

 

 

Blog 33: Important Ideas about Exponential Functions

imageExponential functions have many different steps to them, but there are a few main concepts to understand. The main equation for these types of graphs is y=b^x. One of the main concepts to exponential functions is, an increasing function is a whole number and a decreasing function is only a decimal. Another is, the greater the value of b, the steeper the slope. These are only basic, main points, but there are many more to learn.