Textbook Question
In Exercises 1–30, find the domain of each function. h(x) = 4/(3/x - 1)
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Ch. 2 - Functions and Graphs
Chapter 3, Problem 16
In Exercises 1-16, use the graph of y = f(x) to graph each function g. 
g(x) = -f(2x) - 1
Verified Solution
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Key Concepts
Here are the essential concepts you must grasp in order to answer the question correctly.
Function Transformation
Function transformations involve altering the graph of a function through shifts, stretches, compressions, or reflections. In this case, the function g(x) = -f(2x) - 1 represents a vertical reflection, horizontal compression, and downward shift of the original function f(x). Understanding these transformations is crucial for accurately graphing the new function.
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4:22
Domain & Range of Transformed Functions
Horizontal Compression
A horizontal compression occurs when the input of a function is multiplied by a factor greater than 1, which in this case is the '2' in g(x) = -f(2x). This transformation effectively reduces the width of the graph, making it appear 'narrower' as the x-values are scaled down, resulting in a faster increase or decrease in the function's output.
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5:28Horizontal Parabolas
Vertical Reflection and Shift
A vertical reflection flips the graph of a function over the x-axis, which is represented by the negative sign in g(x) = -f(2x). Additionally, the '-1' at the end of the function indicates a vertical shift downward by one unit. Together, these transformations change the orientation and position of the graph, which is essential for accurately plotting g(x).
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4:25Graphs of Shifted & Reflected Functions
Related Practice
Textbook Question
In Exercises 1-16, use the graph of y = f(x) to graph each function g. g(x) = −ƒ( x/2) +1
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Textbook Question
In Exercises 1–30, find the domain of each function. f(x) = 1/[3/(x - 1) - 2]
243
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Textbook Question
In Exercises 17-32, use the graph of y = f(x) to graph each function g. g(x) = f(x) - 1
241
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Textbook Question
In Exercises 1–30, find the domain of each function. f(x) = √(x - 3)
313
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Textbook Question
In Exercises 17-32, use the graph of y = f(x) to graph each function g. g(x) = f(x-1)
227
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