Question

Write a function g whose graph represents a translation 3 units down followed by a vertical shrink by a factor of 1/3
of the graph of f(x) = x

Answer 1

  If a function 'f' is translated by 'k' units down, image function 'g' will be,

• g(x) = h(x) - 3

If the function 'g' gets shrink by a factor 'm', the new function 'k' will be,

• k(x) = $m[g(x)]$  where, 0 < m < 1

  Following these rules image of the function 'f' given in the question will be g(x) = $\frac{1}{3}x-1$

Function given in the question is,

• f(x) = x

  If the function f is translated by 3 units down, image function 'h' will be,

h(x) = f(x) -3

h(x) = x - 3

  If the image function is vertically shrink by a factor of k, equation of the image function will be,

g(x) = $k[h(x)-3]$

where, k = $\frac{1}{3}$,

g(x) = $\frac{1}{3}}(x-3)$

      = $\frac{1}{3}x-1$

    Therefore, image function will be $g(x)=\frac{1}{3}x-1$.

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