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harkovskaia [24]
3 years ago
8

Enter the Correct answer in the box. Function g is graphed here. [see image] If function f is the parent exponential function f(

x) = e^x , what is the equation of transformed function g in terms of function f? Replace the value of a to complete the equation.

Mathematics
2 answers:
andrey2020 [161]3 years ago
4 0

Answer:

  • g(x) = 1.1f(x + 1)

Step-by-step explanation:

g(x) is the translation of the parent function f(x) to left by 1 unit and slightly stretched vertically.

<u>g(x) is:</u>

  • f(x) = 1.1f(x + 1)

<em>See attached with both graphs included</em>

omeli [17]3 years ago
3 0

Answer:

g(x)=3f(x)

Step-by-step explanation:

the f(x) creates the exact slope of those in the picture because is the parent function of g(x) and by adding the 3 in the front it set the y-intercept to be 3 as such in the picture visual.

-Also if you don't believe me you can always put it in a graphing calculator such as Desmos

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Find the derivative.
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Answer:

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General Formulas and Concepts:

<u>Algebra I</u>

Terms/Coefficients

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Derivative Rule [Quotient Rule]:                                                                           \displaystyle \frac{d}{dx} [\frac{f(x)}{g(x)} ]=\frac{g(x)f'(x)-g'(x)f(x)}{g^2(x)}

Step-by-step explanation:

<u>Step 1: Define</u>

<em>Identify</em>

\displaystyle f(x) = \frac{\sqrt{x}}{e^x}

<u>Step 2: Differentiate</u>

  1. Derivative Rule [Quotient Rule]:                                                                   \displaystyle f'(x) = \frac{(\sqrt{x})'e^x - \sqrt{x}(e^x)'}{(e^x)^2}
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  4. Simplify:                                                                                                         \displaystyle f'(x) = \frac{\frac{e^x}{2\sqrt{x}} - \sqrt{x}e^x}{e^{2x}}
  5. Rewrite:                                                                                                         \displaystyle f'(x) = \bigg( \frac{e^x}{2\sqrt{x}} - \sqrt{x}e^x \bigg) e^{-2x}
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Topic: AP Calculus AB/BC (Calculus I/I + II)

Unit: Differentiation

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