Mathematics and Calculations
Transformation: The graph is shifted one unit to the right
b) jx=x+3
Transformation: The graph is shifted two units to the left
c) hx=x+3
Transformation: The graph is shifted three units along the x axis
d) gx=  x
Transformation: the graph is transformed at an angle of 1800
2. Since no real numbers can be a square root of a negative number, the domain of f consist of all real numbers x such that;
4x+12 0
Therefore determining the domain of f is the same as solving the inequality
Let
hx= 4x+12 0 hx= 4x+12
4x=12
x 3
D= [3, )
Therefore the domain of f is all real numbers in the closed interval of 3 and infinity Set the denominator to zero (0) x+12=0x=12 The domain therefore is all real numbers greater than or less than 12
D= [ , 12) In this case there are no denominators therefore there is no division by zero
There is also no radical therefore there is no square root of a negative
Therefore the domain will be all real numbers The domain will be all real numbers except 0
This is because 1/0 is undefined
[15, ) x15 0 x 15
3. Vertical asymptotes
Steps
The function for the vertical asymptote is first written down. In normal cases it should be a rational function and it should have a variable x in its denominator. Always the vertical asymptote occurs when the denominator of the rational function is nearing zero
The second step is to find the value of x which makes the denominator…

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