Transformations of Power Functions With Positive Integer Index (VCE SSCE Mathematical Methods): Quizzes

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Transformations of Power Functions With Positive Integer Index
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What is the transformation form of a power function with positive integer index?

y=a(xh)n+ky = a(x - h)^n + k

In y=a(xh)n+ky = a(x - h)^n + k, what does a negative value of aa indicate?

A reflection in the xx-axis

What is a key characteristic of odd power functions like f(x)=x3f(x) = x^3?

Always increasing

Even power functions like f(x)=x4f(x) = x^4 are symmetric about which line?

The yy-axis

For y=a(xh)n+ky = a(x - h)^n + k where nn is odd, what is at point (h,k)(h, k)?

Point of zero gradient

For y=a(xh)n+ky = a(x - h)^n + k where nn is even, what is at point (h,k)(h, k)?

Turning point

At which xx values do xnx^n and xmx^m (same parity) always intersect?

x=1,0,1x = -1, 0, 1

For odd power f(x)=xnf(x) = x^n with n3n ≥ 3, what is true about f(x)f'(x) when x0x ≠ 0?

f(x)>0f'(x) > 0 for all x0x ≠ 0

For even power f(x)=xnf(x) = x^n, where is the function decreasing?

For x<0x < 0

If y=a(xh)3+ky = a(x - h)^3 + k has zero gradient at (2,5)(2, 5), what are hh and kk?

h=2,k=5h = 2, k = 5

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