
Concept explainers
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.
53.

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 53AYU
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 square root function.
square root function
Step 2: To obtain the graph of , replace by from each on the graph of , that it is shifted right 2 units.
replace by ; Horizontal shift right 2 units.
Step 3: To obtain the graph of , multiply each of the graph of , by 2, that it is vertically stretched by the factor of 2.
Multiply by 2, vertically stretched by a factor of 2
Step 4: To obtain the graph of , add 1 from each on the graph of , that it is shifted up 1 unit.
add 1, vertically shift up 1 unit.
Interpretation:
Domain of the function is .
Range of the function is .
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Precalculus
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