To graph: The function f ( x ) = x + 2 , using the techniques of shifting, compressing, stretching, and/or reflecting. Start 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.
To graph: The function f ( x ) = x + 2 , using the techniques of shifting, compressing, stretching, and/or reflecting. Start 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.
To graph: The function f(x)=x+2, using the techniques of shifting, compressing, stretching, and/or reflecting. Start with the graph of the basic function (for example, y=x2 ) 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
Answer to Problem 43AYU
Solution:
Domain of the function f(x)=x+2 is [−2,∞)
Range of the function f(x)=x+2 is [0,∞)
Explanation of Solution
Given:
f(x)=x+2
Graph:
Now use the following steps to obtain the graph of f(x) .
Step 1: The function f(x)=x is the square root function.
f(x)=x square root function
Step 2: To obtain the graph of f(x)=x+2, replace x by x+2 from each y-co-ordinate on the graph of f(x)=x, that it is shifted left 2 units
f(x)=x+2 replacex by x+2; Horizontal shift left 2 units.
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