LauraTh3T3ddyB3ar
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I need to write these description into the new function but I keep getting the wrong thing -.-

1.The function f(x)=(1/2)^x is translated 4 units right, reflected across the x-axis, and vertically stretched by a factor of 1.5

2.The function f(x)=ln x is translated 3 units left, horizontally compressed by a factor of 1/4 and translated 0.5 units down.

3. The function f(x)=e^x is horizontally stretched by a factor of 3, reflected across the y-axis, and translated 1 unit right.

Respuesta :

sqdancefan
Since you're studying this stuff, you know that
.. translation right by k units: f(x) ⇒ f(x-k)
.. translation up by k units: f(x) ⇒ f(x) +k
.. horizontal stretch by a factor of k: f(x) ⇒ f(x/k) . . . . same as compressed by 1/k
.. vertical stretch by a factor of k: f(x) ⇒ k*f(x)
.. reflection across the x-axis: f(x) ⇒ -f(x)
.. reflection across the y-axis: f(x) ⇒ f(-x)
The sequence in which these are done is important.

1. f(x) = (1/2)^x
.. translated 4 units right: f(x) = (1/2)^(x -4)
.. reflected across the x-axis: f(x) = -(1/2)^(x -4)
.. vertically stretched by a factor of 1.5: f(x = -1.5(1/2)^(x -4)

2. f(x) = ln(x)
.. translated 3 units left: f(x) = ln(x +3)
.. horizontally compressed by a factor of 1/4: f(x) = ln(x/4 +3)
.. translated down 0.5 units: f(x) = -0.5 +ln(x/4 +3)

3. f(x) = e^x
.. horizontally stretched by a factor of 3: f(x) = e^(x/3)
.. reflected across the y-axis: f(x) = e^(-x/3)
.. translated 1 unit right: f(x) = e^(-(x -1)/3)

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