The function: f(x)=ex+1−2 a) Domain b) Range c) x, y-intercepts d) Sketch a graph of f e) What transformations happened to y=ex to get f(x)?

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The function:  f(x)=ex+1−2  a) Domain  b) Range  c) x, y-intercepts  d) Sketch a graph of f  e) What transformations happened to y=ex to get f(x)?

Branden Nelson · Accepted Answer

Step 1  a) now y=ex+1−2  domain is the set of all value of x for which f(x) is defined.  hence domain of f(x) is  R i.e. (−∞,∞) or all real numbers.  b) set of all value of y which we get.  Now y=ex+1−2  ⇒y+2=ex+1  Since ex+1&amp;gt;0  ⇒y+2&amp;gt;0  range {y∈R:y≻2} or  range y∈(−2,∞)

dicky23628u6a · Accepted Answer

Step 1  c) y=ex+1−2  for x-intercept  put y=0  ⇒ex+1−2=0  ex+1=2  ln⁡(e(x+1)}=ln⁡(2)  (x+1)ln⁡(e)=0.6931  x+1−0.6931  x=0.6931−1  x=−0.307  for y-intercept  put x=0  y=e0+1−2  y=e−2  y=2.7183−2  y=0.718  d) Sketch the graph of f(x)=ex+1−2    e) what Tran-formation happen to y=ex to get f(x)=ex+1−2  tansformation: along y-axis 2 unit upward.  along x-axis stretch the curve vertically by e=2.718    red color graph =f(x)=ex+1−2  blug graph y=ex

The function: f(x)=e^{x+1}-2 a) Domain b) Range c) x, y-intercepts d) Sketch a graph of

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