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# P04SelectedAnswers - g give its domain in interval notation...

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Project 4 MAC 2311 1. How can the graph of the function f ( x ) = ( 1 2 ) x be obtained from the graph of y = 2 x ? Illustrate by drawing both graphs on the axes. . Given a constant a , what rule would represent the the graph of f ( x ) reﬂected across the line y = a ? x = a ? x = a , e.g., new rule is f ( - ( x - a ) + a ) = f (2 a - x ) 2. Carefully sketch the graph of f ( x ) = 1+ e 1 - x below , including any intercepts and asymptotal lines, AND state its domain and range in interval notation. Domain: Range: Consider steps: e x e x +1 e ( - x )+1 -→ 1 + e 1 - x Now suppose g ( x ) is the function obtained by reﬂecting the graph of f ( x ) across the x -axis and then shifting the resulting graph up two units. Carefully sketch the graph of g ( x ) below , including any intercepts and asymptotal lines, AND state its domain and range in interval notation. Also, write an algebraic formula for g ( x ) . Domain: ( -∞ , ) Range: ( -∞ , 1 ) Formula: g ( x ) = 1 - e 1 - x

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3. This problem uses the functions below: f ( x ) = x 2 g ( x ) = 1 - x 2 h ( x ) = 1 - x Write a simpliﬁed formula for the function k = f + g ·
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Unformatted text preview: g ; give its domain in interval notation. Write a simpliﬁed formula for the function k = ( f + g ) ◦ h ; give its domain in interval notation. k ( x ) = 1-x + √ x ; Domain: [ 0 , 1 ] 4. A rectangle is fashioned so that its area and perimeter have the same numeric value. Write the length ‘ of the rectangle as a function of the width w . What is the only square that behaves this way? 5. A company manufactures a gutter by bending up the sides of a metal sheet of ﬁxed width w = 2 ft, so that cross-sections form an isosceles trapezoid with desired length b = 1 ft for the smaller base as shown. Express the cross-sectional area as a function of the angle θ . For fun, experiment with a calculator to try to decide what θ maximizes the cross-sectional area. note that the triangle shown has sides 1 2 sin( θ ) and 1 2 cos( θ )...
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P04SelectedAnswers - g give its domain in interval notation...

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