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Graph transformations

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State the placement of the horizontal asymptote and y-intercept after the transformation. For example, left 1 or rotated about the y-axis are descriptions.
a) g(x)=e^x-5
description of transformation:
equation(s) for the horizontal asymptote(s):
y-intercept in (x,y) form:
b) h(x)=-e^x
description of transformation:
equation(s) for the horizontal asymptote(s):
y-intercept in (x,y) form:

Describe the transformation on the following graph of f(x)=log(x)
placement of the vertical asymptote and x-intercept after the transformation, for example, left 1 or stretched vertically by a factor of 2 are descriptions.
a) g(x)=log(x-3)
description of transformation:
equation(s) for the vertical asymptote(s):
x-intercept in (x,y) form:
b) g(x)=log(x)
description of transformation:
equation(s) for the vertical asymptote(s):
x-intercept in (x,y) form:

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Solution Summary

This provides several examples of graph transformations based on asymptotes and intercepts.

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a) g(x)=e^x-5
description of transformation: Slide down 5

equation(s) for the horizontal asymptote(s): As x decreases without bound, f(x) = ex - 5 approaches - 5. The graph of g has a horizontal asymptote y=- 5.

y-intercept in (x,y) form: (0, -4)

b) ...

Solution provided by:
Sandhya Sharma, MSc
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  • BSc, Meerut University
  • MSc, Meerut University
  • MPhil, Institute of Advanced Studies
  • MSc, AIT
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