University:
Washington State University
Course:
MATH 172 | Calculus II
Academic year:

2024
Views:

78

Pages:

2
Author:

Bailey Ayala

Question 1 Explain how transformations, families of functions, and parent functions are related. Answer Parent functions are the basic building block functions like y=x y = x² y = √x etc. that can be transformed into families of functions using transformations such as translations, scakking (compressin, strching), and reflections. Question 2 How can you use what you know about transformations of functions to graph radical functions? Answer All that we used in transformations of graphs of linear and square functions, can be applyed to the graphs of radical functions. If we are adding or subtracting a number from the x, than the function will translate left and right. If we are adding or subtracting a number from the y, than the function will translate up and down. Same goes for reflecting given functions across x-axis, y-axis and the (0,0) point. Question 3 In your own words, summarize the guidelines for finding limits at infinity of rational functions. Answer The following are the guidelines for finding limits at infinity of rational functions. Ifthe degree of the numeratoris less than the degree of the denominator, the the limit at infinity is 0 If the degree of the numerator is greater than the degree of the denominator, the the limit at infinity does not exist Ifthe degree of the numeratoris equal tothe degreeof the denominator, the limit is equal to the ratio of the leading coefficients. Question 4 Begin with the graph of y = ln x and use transformations to sketch the graph of each of the given functions. y = 1 - ln(1 - x) Answer Replacing x with -x in ln x reflects the graph about the y-axis. Replacing -x with 1-x in ln(-x) shifts the graph 1 unit right. Multiplying ln(1-x) by -1 reflects the graph about the x-axis. Adding 1 to - ln(1-x) shifts the graph 1 units up. Question 5 Sketch a graph of the function. Use transformations of functions when ever possible. f(x) = 1 + √x Answer Step 1 We are given the function: f(x) = 1 + √x Step 2 Build a table of values: | x | f(x) | |---|---| | 0 | 1 | | 1 | 2 | | 4 | 3 | | 9 | 4 | | 16 | 5 | | 25 | 6 | Step 3 Plot the points and join them by a curve: [Image of a hand-drawn graph with points plotted at (0,1), (1,2), (4,3), (9,4), (16,5), and (25,6).]