Transformation of graphs
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1) Describe the transformations on the following graph of f(x) = e^x . 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 - 2
b) h(x) = - e^x
2) Describe the transformations on the following graph of f(x) = log(x). State the 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)
b) g(x) = log(-x)
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Solution Summary
The solution is comprised of detailed step-by-step explanations of transformations on two types of functions: exponential function and logarithmic function
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Describe the transformations on the following graph of . 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)
Description of transformation: down 5 units, that is, move downward by 5 units to obtain g(x).
Equation(s) for the Horizontal asymptote(s): The horizontal asymptote of is the x-axis, or y = 0. So the horizontal asymptote of g(x) is , which is obtained by shifting y = 0 downward by 5 units.
y-intercept in (x, y) form: when x = 0, .
so y-intercept is (0, -4).
The y-intercept of is ...
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