Which of the following transformations are linear? Select all of the linear transformations. There may be more than one correct answer. Be sure you can justify your answers. A. $T (f (t)) = f^{?} (t) + 9 f (t) + 6$ from $C^{?}$ to $C^{?}$ B. $T (f (t)) = f (4)$ from $P_{8}$ to $R$ C. $T (f (t)) = t^{3} f^{?} (t)$ from $P_{2}$ to $P_{4}$ D. $T (f (t)) = ?_{? 7}^{9} f (t) d t$ from $P_{6}$ to $R$ E. $T (f (t)) = f (t) f^{?} (t)$ from $P_{7}$ to $P_{13}$ F. $T (f (t)) = f (? t)$ from $P_{2}$ to $P_{2}$

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Which of the following transformations are linear? Select all of the linear transformations. There may be more than one correct answer. Be sure you can justify your answers. A.

T (f (t)) = f^{?} (t) + 9 f (t) + 6

from

C^{?}

to

C^{?}

B.

T (f (t)) = f (4)

from

P_{8}

to

R

C.

T (f (t)) = t^{3} f^{?} (t)

from

P_{2}

to

P_{4}

D.

T (f (t)) = ?_{? 7}^{9} f (t) d t

from

P_{6}

to

R

E.

T (f (t)) = f (t) f^{?} (t)

from

P_{7}

to

P_{13}

F.

T (f (t)) = f (? t)

from

P_{2}

to

P_{2}

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