Student problem #4

 

This problem is about graphing logarithmic functions and identifying x- intercepts, y intercepts, asymptote, domain, and range.

The reader must remember that the graph continues on forever in both directions. Also, graphing calculators are just unable to show the graph close to the asymptote. Make sure to draw arrows on both ends.

Student Video #6: Compund Interest

 

What is this video about?

This video is about calculating compund interest and all the different parts and factors that we use to solve for it. These factors are our current amount of money, the principal amount, rate, number of times per year compunded, and the amount of time in years.

What does the viewer need to pay special attention to in order to understand the concept?
         -Notice the two different formulas and what they are used for. Also, look out for the part where you learn how to convert months to years using the information you calculated.
        

Student Problem #3 Exponential Functions

 

 

1) What is the problem about?
This problem covers an example from unit I concept 1. This picture covers how to graph exponential functions and identifying the x-intercept, y-intercept, asymptotes, domain, and range.

2) What must the reader pay close attention to in order not to make a mistake?
Make sure to notice how the equation is set up. The general set up for an exponential function is y=a(b^x-h)+k. If a is positive, the graph will be above the asymptote. If a is negative, the graph will be below the asymptote. If the absolute value of b is less than 1, the graph is close to the asymptote on the right side. If the absolute value of b is greater than 1, the graph is close to the asymptote to the left side. H shifts the graph left and right and in our case, our key points will do the shifting for us. If k is positive, it moves the asymptote up "k" units. If k is negative, it moves the asymptote down "k" units.

Student Video #3 Unit H Concept 7

What is this video about?
-This video covers a problem from Unit H Concept 7 which covers how to find logs given approximations. In this video, we review how to expand our clues using the properties of logs.

What does the viewer need to pay special attention to in order to understand the concept?
-Look at how we used the prime factor tree to break down what we were trying to find. Factoring makes doing these problems so much easier.
-Notice how we substituted the variables for the logs once found the logs.

Unit G Summary Question #10 Range of a Rational Function

The range of a rational function depends on the y values of the domain. Range is horizontal asymptotes and holes. For example, y = (3x - 4)/(1+2x)
(1 + 2x)y = 3x - 4
y + 2xy - 3x = 4
2xy - 3x = 4 - y
(2y - 3)x = 4 - y
x = (4 - y)/(2y - 3). Domain is finding the x values while range is finding the y values. In this case, we solve for y to get our range. Domain and range go hand in hand because they depend on each other. The y of the domain is the range and the x of the range is the domain.



Unit G Summary Question #9 x intercepts of rational functions

To find the x intercepts of rational functions, obviously we have to plug in 0 as our y. For example, x^2-4x-4/ x^2+6x+9. If we plug in zero as our y, then we have a ratio. (0/1)=(x^2-4x-4)/(x^2+6x+9). When we cross multiply, the denominator becomes zero and the numerator factors into (x-2)(x-2). We then set this to zero and our x intercepts is 2 multiplicity 2. The shortcut is basically factoring the numerator and setting it to zero. This makes more sense because if you were to find the x intercept the long way, then you would still get to this point but not until after you've done some unnecessary work. It takes less time and is easy to do.



Unit G Summary Question #8 y-intercepts of rational functions

To describe the y intercept of a rational function, we first need an example.                                        For example, x^2-4/x^2-1. We all know that in order to find the y intercept of anything, we must first plug in zero to EVERYTHING! Here, if we do that, we get 4/1 which is 4 and our y intercept is 0,4. Basically, in this case, you divide the constants numerator over denominator. It can be done both in the original equation or the simplified equation because you would still have to plug in zezro to find your y.