# A-level Mathematics C3 Formulae

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09 October 20:03

# $y\; =\; -f\; left\; (x$

ight ), is a absorption of $y\; =\; f\; left\; (x$

ight ), through the x axis.

# $y\; =\; f\; left\; (-x$

ight ), is a absorption of $y\; =\; f\; left\; (x$

ight ), through the y axis.

#$y\; =\; eginfleft(x$

ight)end is a absorption of $y\; =\; f\; left\; (x$

ight ), if y < 0, through the x-axis.

#$y\; =fleft(eginxend$

ight) is a absorption of $y\; =\; f\; left\; (x$

ight ), if x > 0, through the y-axis.

# $y\; =\; f^\; left\; (x$

ight ), is a absorption of of $y\; =\; f\; left\; (x$

ight ), through the band y=x. $y\; =\; f\; left\; (x$

ight ), haveto accept a 1:1 mapping.

# $y\; =\; f\; left\; (bx$

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.

# $y\; =\; af\; left\; (x$

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.

# $y\; =\; f\; left\; (x\; -\; h$

ight ), is a adaptation of f(x) by h units to the right.

# $y\; =\; f\; left\; (x\; +\; h$

ight ), is a adaptation of f(x) by h units to the left.

# $y\; =\; f\; left\; (x$

ight ) + k, is a adaptation of f(x) by k units upwards.

# $y\; =\; f\; left\; (x$

ight ) - k, is a adaptation of f(x) by k units downwards.

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

#$yleft(t$

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:

::

By the end of this bore you will be accepted to accept learnt the afterward formulae:# $y\; =\; -f\; left\; (x$

ight ), is a absorption of $y\; =\; f\; left\; (x$

ight ), through the x axis.

# $y\; =\; f\; left\; (-x$

ight ), is a absorption of $y\; =\; f\; left\; (x$

ight ), through the y axis.

#$y\; =\; eginfleft(x$

ight)end is a absorption of $y\; =\; f\; left\; (x$

ight ), if y < 0, through the x-axis.

#$y\; =fleft(eginxend$

ight) is a absorption of $y\; =\; f\; left\; (x$

ight ), if x > 0, through the y-axis.

# $y\; =\; f^\; left\; (x$

ight ), is a absorption of of $y\; =\; f\; left\; (x$

ight ), through the band y=x. $y\; =\; f\; left\; (x$

ight ), haveto accept a 1:1 mapping.

# $y\; =\; f\; left\; (bx$

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.

# $y\; =\; af\; left\; (x$

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.

# $y\; =\; f\; left\; (x\; -\; h$

ight ), is a adaptation of f(x) by h units to the right.

# $y\; =\; f\; left\; (x\; +\; h$

ight ), is a adaptation of f(x) by h units to the left.

# $y\; =\; f\; left\; (x$

ight ) + k, is a adaptation of f(x) by k units upwards.

# $y\; =\; f\; left\; (x$

ight ) - k, is a adaptation of f(x) by k units downwards.

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

#$yleft(t$

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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