The function below models the monthly revenue R(x) (in thousands of dollars) of a local landscaping business for the year 2019. The independent variable, x, corresponds to each month, with x = 1 representing January of that year. R(t)= 30-3 |2x - 12| The goal is to graph this function and analyze and interpret the graph in this problem context. a) What is the mathematical domain of this function? Express your answer in interval notation: By inspecting the function, describe the shape and orientation of the graph of this function. Explain your reasoning. b) Rewrite this function algebraically in transformation form: Construct the tables showing the mapping of three points (0,0), (-2,2), and (2,2) from the basic function: Sketch this function using the method of transformations. Your graph should be hand-drawn on graph paper, using no more than 1/3 of the page. Label the axes and clearly show the scale on the axes.

The function below models the monthly revenue R(x) (in thousands of dollars) of a local landscaping business for the year 2019. The independent variable, x, corresponds to each month, with x = 1 representing January of that year. R(t)= 30-3 |2x - 12| The goal is to graph this function and analyze and interpret the graph in this problem context. a) What is the mathematical domain of this function? Express your answer in interval notation: By inspecting the function, describe the shape and orientation of the graph of this function. Explain your reasoning. b) Rewrite this function algebraically in transformation form: Construct the tables showing the mapping of three points (0,0), (-2,2), and (2,2) from the basic function: Sketch this function using the method of transformations. Your graph should be hand-drawn on graph paper, using no more than 1/3 of the page. Label the axes and clearly show the scale on the axes.

Calculus: Early Transcendentals

8th Edition

ISBN:9781285741550

Author:James Stewart

Publisher:James Stewart

Chapter1: Functions And Models

Section: Chapter Questions

Problem 1RCC: (a) What is a function? What are its domain and range? (b) What is the graph of a function? (c) How...

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Question

The function below models the monthly revenue R(x) (in thousands of dollars) of a local landscaping
business for the year 2019. The independent variable, x, corresponds to each month, with x = 1
representing January of that year.
R(t)= 30-3 |2x - 12|
The goal is to graph this function and analyze and interpret the graph in this problem context.
a) What is the mathematical domain of this function?
Express your answer in interval notation:
By inspecting the function, describe the shape and orientation of the graph of this function. Explain
your reasoning.
b) Rewrite this function algebraically in transformation form:
Construct the tables showing the mapping of three points (0,0), (-2,2), and (2,2) from the basic function:
Sketch this function using the method of transformations. Your graph should be hand-drawn on graph
paper, using no more than 1/3 of the page. Label the axes and clearly show the scale on the axes.

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Follow-up Questions

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Follow-up Question

c) Find the R and x intercepts of this function and plot these points on your graph.
d) State the practical domain in interval notation:
e) Logically interpret the shape of the graph in this problem context. ie. What does the graph tell us
about this scenario?
f) Express this function in piecewise-defined form on the practical domain. (Hint: First find the
equations of the two lines on the graph in y = mx + b form.) Fill in the piecewise form below.
R(x) = {
1≤x≤6
6 < x≤ 12

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