Look at the graph below carefully
Observe the results of shifting ={2}^{x}f(x)=2x
vertically:
The domain, (−∞,∞) remains unchanged.
When the function is shifted up 3 units to ={2}^{x}+3g(x)=2x +3:
The y-intercept shifts up 3 units to (0,4).
The asymptote shifts up 3 units to y=3y=3.
The range becomes (3,∞).
When the function is shifted down 3 units to ={2}^{x}-3h(x)=2 x −3:
The y-intercept shifts down 3 units to (0,−2).
The asymptote also shifts down 3 units to y=-3y=−3.
The range becomes (−3,∞).
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Answer:
Step-by-step explanation:
The transformation ...
g(x) = a×f(x-h) +k
performs a vertical stretch by the factor 'a', and a translation by (h, k), which is h units right and k units up. When 'a' is negative, there is a reflection over the x-axis.
Here, we have 'a' = -1, h = 3, k = 'e'. So, the graph of f(x) has been ...
reflected over the x-axis
translated right by 3 units
translated up by 'e' units
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<em>Additional comment</em>
We don't know if your 'e' is a typo. When talking about exponential functions, 'e' often refers to the base of natural logarithms, an irrational number approximately equal to 2.718281828459045...
Here's a graph of an exponential function transformed as you have indicated.
