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.
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 Problem #5
What is this about?
-This picture shows an example of partial fraction decomposition with distinct factors. It is an algebraic skill essential to certain aspects for integration in Calculus. While we know how to add fractions together by finding a common denominator, we will learn how to decompose, or break fractions apart.
What does the viewer need to pay special attention to in order to understand the concept?
-The viewer needs to pay special attention to the steps that this system requires to decompose. These steps include how to multiply parts to find a least common denominator and also how to combine like terms. The viewer also needs to pay attention to how the like terms are taken and made into systems, which can now be solved depending on the number of systems as well as other factors. These methods are algebra 2 skills and matrices.
Student Problem #6
What is this about?
-This picture shows an example of partial fraction decomposition with repeated factors. It is an algebraic skill essential to certain aspects for integration in Calculus. While we know how to add fractions together by finding a common denominator, we will learn how to decompose, or break fractions apart.
What does the viewer need to pay special attention to in order to understand the concept?
-The viewer needs to pay special attention to how to deal with repeated factors. This means that each factor must be separated into separate fractions. For the repeated factor, you must count up the powers and include the factor as many times as the exponent.
Student Problem #7
What is this about?
-this picture shows an example of how to write a repeating decimal as a rational number using geometric series. Because it is very easy to do, no calculator will be necessary. While doing this, we will learn what certain variables stand for.
What does the viewer need to pay special attention to in order to understand his concept?
-The reader needs to pay special attention to how to divide fractions and multiplying the reciprocal when it comes to the sum of the series. Keep in mind that the formulas used here are just for these types of problems because there are so many, it's easy to get confused.
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