In Problems 39-62, graph each function using the techniques of shifting, compressing, stretching, and/or reflecting. Stan with the graph of the basic function (for example, y = x 2 ) and show all stages. Be sure to show at least three key points. Find the domain and the range of each function. f ( x ) = ( x + 2 ) 3 - 3
In Problems 39-62, graph each function using the techniques of shifting, compressing, stretching, and/or reflecting. Stan with the graph of the basic function (for example, y = x 2 ) and show all stages. Be sure to show at least three key points. Find the domain and the range of each function. f ( x ) = ( x + 2 ) 3 - 3
In Problems 39-62, graph each function using the techniques of shifting, compressing, stretching, and/or reflecting. Stan with the graph of the basic function (for example,
) and show all stages. Be sure to show at least three key points. Find the domain and the range of each function.
Expert Solution & Answer
To determine
To graph: The function , using the techniques of shifting, compressing, stretching, and/or reflecting. Start with the graph of the basic function (for example, ) and show all stages. Be sure to show at least three key points. Find the domain and the range of each function.
Answer to Problem 46AYU
Domain of the function is .
Range of the function is .
Explanation of Solution
Given:
Graph:
Now use the following steps to obtain the graph of .
Step 1: The function is the cube function.
cube function
Step 2: To obtain the graph of , replace by from each on the graph of , that it is shifted left 2 units.
replace by ; Horizontal shift left 2 units.
Step 3: To obtain the graph of , subtract 3 from each on the graph of , that it is shifted down 3 units.
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