Power Functions (VCE SSCE Mathematical Methods): Quizzes

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Power Functions
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What is the general form of a power function?

f(x)=xrf(x) = x^r where rr is rational

What type of symmetry does f(x)=x4f(x) = x^4 have?

Reflective symmetry about y-axis

What is the maximal domain of f(x)=x14f(x) = x^{\frac{1}{4}}?

R+{0}\mathbb{R}^+ \cup \{0\}

What is the range of f(x)=x6f(x) = x^6?

R+{0}\mathbb{R}^+ \cup \{0\}

What are the asymptotes of f(x)=x3f(x) = x^{-3}?

x=0x = 0 and y=0y = 0

For odd positive integer nn, how does f(x)=xnf(x) = x^n behave?

Strictly increasing everywhere

What is the value of 8138^{\frac{1}{3}}?

22

What is the range of f(x)=x2f(x) = x^{-2}?

R+\mathbb{R}^+

For f(x)=x5f(x) = x^5, what is f(1)f(-1)?

1-1

If ff is odd and one-to-one, what about f1f^{-1}?

f1f^{-1} is also odd

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