Math 143 Week 7 Homework !!

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University of Hawaii *

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143

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Mathematics

Date

Apr 3, 2024

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pdf

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4

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M143 Week 7 Worksheet Worksheet Assignment Cubic Regression Directions: These activity questions are written to follow the activity for the week. After the weekly lecture class meetings, you should be able to answer these questions. Answer the questions, save the document, and submit the assignment to Canvas. 1. If the leading coefficient of a cubic function is positive, what do you know about the graph of the cubic function? The leading coefficient (term with the highest power) indicates the end behavior of the graph. Since we know that the leading coefficient is positive, we can determine that the graph would be increasing (infinitely) to the right side of the graph. 2. When making observations, collecting and using data, there are typically limitations as to how far data can be used to make predictions. Which math 143 topic below best describes limitations. Explain your selection. a) Linear, quadratic, cubic equations b) Maximum and Minimums c) Domains and Ranges d) x -intercepts I believe that Domains and Ranges (Answer C) best describes limitations. We have learned from Desmos that domains and ranges can help us identify the limitations of our data. Some data that we put into Desmos, only covers a limited range of input values. By using both domain and range, we can identify the limitations and make predictions on our data collected. 3. How many x-intercepts must a cubic function have? Explain. A cubic function must have a minimum of one x-intercept but may have as many as three. The x-intercepts are related to the roots of the cubic equation that are represented by the function. The number of x-intercepts it has also depends on the function’s behavior as it crosses the x-axis (number of real and complex roots).
M143 Week 7 Worksheet 4. Given the graph below, what is a possible equation for the graph? Explain your process. Y = -x^(3) - 4.3x^(2)+4 is a possible equation for the graph because it is a cubic function, which means we are going to have to begin with a cubed coefficient. We can also locate our value of K, which is equal to 4! Our function is decreasing, which means our function will be negative. 5. Using the graph in #4, locate the maximum and minimum value(s), if they exist. Explain how you determine whether you have a maximum or minimum value. Our local minimum value is roughly (-1, -8) and our local maximum value is roughly (2, 4). If we were to look outside of our “local values”, our minimum value would be negative infinity and our maximum value would be positive infinity. 6. Explain what it means for a relation to be a function. Sketch the graph of a relation that is a function. Give a set of ordered pairs that do NOT represent a function. A function of a relation is the point at which each information has just a single result. A function can’t have two similar x-values. This is a set of ordered pairs that do not represent a function: X = 4, 8, 4 (similar x-values) Y = 1, 3, 2
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