# A-level Mathematics C3 Formulae

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09 October 20:03   By the end of this bore you will be accepted to accept learnt the afterward formulae:

# $y = -f left \left(x$
ight ), is a absorption of $y = f left \left(x$
ight ), through the x axis.

# $y = f left \left(-x$
ight ), is a absorption of $y = f left \left(x$
ight ), through the y axis.

#
ight)end is a absorption of $y = f left \left(x$
ight ), if y < 0, through the x-axis.

#
ight) is a absorption of $y = f left \left(x$
ight ), if x > 0, through the y-axis.

# $y = f^ left \left(x$
ight ), is a absorption of of $y = f left \left(x$
ight ), through the band y=x. $y = f left \left(x$
ight ), haveto accept a 1:1 mapping.

# $y = f left \left(bx$
ight ), is continued appear the y-axis if $0 < b < 1,$ and continued abroad from the y-axis if $b > 1,$. In both cases the change is by b units.

# $y = af left \left(x$
ight ), is continued appear the x-axis if $0 < a < 1,$ and continued abroad from the x-axis if $a > 1,$. In both cases the change is by a units.

# $y = f left \left(x - h$
ight ), is a adaptation of f(x) by h units to the right.

# $y = f left \left(x + h$
ight ), is a adaptation of f(x) by h units to the left.

# $y = f left \left(x$
ight ) + k, is a adaptation of f(x) by k units upwards.

# $y = f left \left(x$
ight ) - k, is a adaptation of f(x) by k units downwards.

#$e^ = ln e^x = x,$

#$yleft\left(t$
ight)=y_0e^,, area y(t) is the final value, $y_0$ is the antecedent value, k is the advance constant, t is the delayed time.

#$k = - frac$, k for calculations involving half-lives.

For volumes of revolution:

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