$\text { Specify a sequence of transformations for the function } h ( x ) = \sin \left( x + \frac { \pi } { 3 } \right) + 7 \text { that }$

question 45

Multiple Choice

$\text { Specify a sequence of transformations for the function } h ( x ) = \sin \left( x + \frac { \pi } { 3 } \right) + 7 \text { that }$ will yield the graph of $h$ from the graph of the function $f ( x ) = \sin x$ .

• A)
• The function \(h ( x ) = \sin \left( x + \frac { \pi } { 3 } \right) + 7\) is a horizontal shift \(\frac { \pi } { 3 }\) units to the right, followed by a vertical shift 7 units downwards.
• B) The function \(h ( x ) = \sin \left( x + \frac { \pi } { 3 } \right) + 7\) is a horizontal shift \(\frac { \pi } { 3 }\) units to the left, followed by a vertical shift 7 units upwards.
• C) The function \(h ( x ) = \sin \left( x + \frac { \pi } { 3 } \right) + 7\) is a horizontal shift \(\frac { \pi } { 3 }\) units to the left, followed by a horizontal shift 7 units to the right.
• D) The function \(h ( x ) = \sin \left( x + \frac { \pi } { 3 } \right) + 7\) is a vertical shift \(\frac { \pi } { 3 }\) units downwards, followed by a horizontal shift 7 units to the right.
• E) The function \(h ( x ) = \sin \left( x + \frac { \pi } { 3 } \right) + 7\) is a vertical shift \(\frac { \pi } { 3 }\) units upwards, followed by a horizontal shift 7 units to the left.

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