Function Notation and Identities (VCE SSCE Mathematical Methods): Flashcards

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Function notation and identities
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Adding logarithms corresponds to what operation on arguments?

Multiplying their arguments

Subtracting logarithms corresponds to what operation?

Dividing their arguments

For f(x)=log⁡exf(x) = \log_e x, what is f(x)+f(y)f(x) + f(y) equal to?

f(xy)f(xy)

For f(x)=exf(x) = e^x, what is f(x+y)f(x + y) equal to?

f(x)f(y)f(x)f(y)

Adding exponents corresponds to what operation?

Multiplying exponential values

Does f(x+y)=f(x)+f(y)f(x+y) = f(x) + f(y) hold for f(x)=2xf(x) = 2x?

Yes, for all values of xx and yy

Does f(x+y)=f(x)+f(y)f(x+y) = f(x) + f(y) hold for f(x)=x+2f(x) = x + 2?

No, the constant term prevents this

For f(x)=1xf(x) = \frac{1}{x}, what is f(x)+f(y)f(x) + f(y) equal to?

(x+y)f(xy)(x + y)f(xy)

How to disprove a property holds for all values?

Find one counterexample

Why must xx and yy be non-zero for f(x)=1xf(x) = \frac{1}{x}?

f(x)=1xf(x) = \frac{1}{x} is undefined at x=0x = 0

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More Power Functions

Composite and Inverse Functions

Sums and Products of Functions and Addition of Ordinates

Function Notation and Identities

Families of Functions and Solving Literal Equations

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