3) Write a formula for the function obtained when the graph is shifted as described. a) \( f _ { x } ) = | x | \) is shifted down \( 3 \) units and to the right \( 1 \) unit. b) \( f _ { x } ) = x ^ { 2 } \) is shifted up \( 1 \) unit and to the left \( 2 \) units. c) \( f _ { x } ) = x ^ { 2 } \) is reflected over the \( x \) -axis and is shifted down \( 2 \) units
a) |x -1| - 3 , b) \((x+ 2)^2+ 1\) , c) \(- x^2- 2\)
If \( y = f ( g ( h ( x ) ) ) , \) then the derivative \( y ^ { \prime } \) is given by which for
a) \( f ^ { \prime } ( g ( h ( x ) ) \)
b) \( f ^ { \prime } ( g ( h ( x ) ) h ^ { \prime } ( x ) \)
c) None of these
d) \( f ^ { \prime } ( g ( h ( x ) ) g ^ { \prime } ( h ( x ) ) \)
e) \( f ^ { \prime } ( g ( h ( x ) ) g ^ { \prime } ( h ( x ) ) h ^ { \prime } ( x )\)
Determine the following limits. If infinite, specify \( \infty \) or \( - \infty \) . If an answer does not exist, explain why. (NO POINTS WILL BE GIVEN IF A TABLE OF VALUES IS USED) b. \( \lim _ { x \rightarrow 1 ^ { + } } [ \frac { x } { x - 1 } + \frac { 1 } { \ln ( x ) } ]\)
