MATH (Tonight, Easy, Pre-calc)
jusinc1
m111_worksheet_2_.pdf
Math 111 Worksheet 2 Name________________________________ Show ALL work. Solutions must satisfy the requirements specified in the Math 111 DOCUMENTATION GUIDELINES.
1) Graph f x x
x x ( ) = − + − ≤ <
− + ≤ <
⎧ ⎨ ⎪
⎩⎪
1 2
6 4
10 1 4
2 x 0
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2) Given f as shown in the Figure below. Sketch and list the sequence of transformations that takes to . )(xf ( ) 4 2 (5 )g x f x= − + −
13
8
y
x 13
8
y
x
Sequence of Transformations:
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x
y
2=y
1−=x 1=x
)0,0( )0,2( x
y
x
y
2=y
1−=x 1=x
)0,0( )0,2(
3) Find a possible formula for the function ( )
( ) ( )
p x r x
q x = given in the graph below. Show all work in
your derivation.
Zeros Graph Mult Factors Behavior
Zeros Graph Mult Factors Behavior
Zeros of p Zeros of q
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4) Tumors are sometimes treated by irradiating them with gamma rays from a radioactive source such as cobalt-60. The intensity of radiation (in milliroentgens per hour, written mr/hr) is proportional to the reciprocal of the distance squared from the source (in meters). Suppose that for a particular source, the intensity is 100 mr/hr at 4 meters. Generate an equation that describes the distance from the source as a function of the intensity of radiation.
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5) Let 1 1
)( − +
= x x
xf and 2
)( +
= x
x xg . Using interval notation, state the domain for ( . Provide
rationale for your solution.
)g f
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