State the various transformations applied to the base function to obtain a graph of the function g(x) = |x + 1| − 2.
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Answer: y = 2x + 6
Step-by-step explanation:
Here the equation of line,
y = 2x + 1
y-intercept of the line is, (0, 1)
And, the slope of the line is 2.
Since, If a point (x,y) is dilated by a scale factor k about a point (a,b),
Then transformed point are get by,
Thus, The transformed point of point (0,1) when dilation is occur by the scale factor 2 about the point (0,-4),
Thus, the point of the new line is (0,6)
And, the slope of the new line is 2 ( because in the dilation, the slope of the line does not change)
Thus, the equation of new line,
(y - 6) = 2 (x - 0)
y - 6 = 2x
y = 2x + 6
