One-to-One Functions and Implied Domains (VCE SSCE Mathematical Methods): Quizzes

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One-to-One Functions and Implied Domains
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What defines a one-to-one function?

Different xx-values give different yy-values

Is {(1,4),(2,2),(3,4),(4,6)}\{(1, 4), (2, 2), (3, 4), (4, 6)\} one-to-one?

No, both x=1x=1 and x=3x=3 map to y=4y=4

Is {(1,4),(2,3),(3,2),(4,1)}\{(1, 4), (2, 3), (3, 2), (4, 1)\} one-to-one?

Yes, each xx maps to a unique yy

What does the horizontal-line test check?

If a function is one-to-one

Is y=x2y = x^2 one-to-one?

No, a horizontal line crosses it twice

Is y=2x+1y = 2x + 1 one-to-one?

Yes, horizontal lines cross it once only

What is the implied domain of f(x)=2x5f(x) = \sqrt{2x - 5}?

[52,)[\frac{5}{2}, \infty)

What is the implied domain of g(x)=12x5g(x) = \frac{1}{2x - 5}?

R{52}\mathbb{R} \setminus \{\frac{5}{2}\}

For square root functions, what must be true?

Expression under root must be 0\geq 0

For rational functions, what restriction applies?

Denominator cannot equal zero

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