Families of Functions and Solving Literal Equations (VCE SSCE Mathematical Methods): Quizzes

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Families of Functions and Solving Literal Equations
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What is a family of functions?

Related funcs w/ same form, diff params

What are parameters in function families?

Constants like mm, kk, aa, bb, cc

For f(x)=mx+2f(x) = mx + 2 where m>0m > 0, what is the x-axis intercept?

2m-\frac{2}{m}

For f(x)=mx+2f(x) = mx + 2 (m>0m > 0), when is the x-intercept less than 2-2?

0<m<10 < m < 1

What is the inverse of f(x)=mx+2f(x) = mx + 2 where m>0m > 0?

f1(x)=1mx2mf^{-1}(x) = \frac{1}{m}x - \frac{2}{m}

What is the gradient of a line perpendicular to one with gradient mm?

1m-\frac{1}{m}

Solve aebxc=0ae^{bx} - c = 0 for xx (all constants positive).

x=1bloge(ca)x = \frac{1}{b}\log_e\left(\frac{c}{a}\right)

Solve loge(xa)=b\log_e(x - a) = b for xx (all constants positive).

x=eb+ax = e^b + a

A quadratic through (1,6)(1, 6) and (2,4)(2, 4) with y-int cc. Find aa in terms of cc.

a=c82a = \frac{c - 8}{2}

Transform (x,y)(5x+5,ky+2)(x,y) \to (5x+5, ky+2) maps y=1xy=\frac{1}{x} through origin. Find kk.

k=2k = 2

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