Question

Let the graph of g be a translation 5 units up followed by a reflection about the y−axis of the graph of f(x)=6x. Write a rule for g.

Answer 1

Reflections and translations are instances of transformation.

The rule of function g for the given reflection and translation is $g(x) =-6x + 5$

Given

$f(x) = 6x$

The rule of translating 5 units up is:

$(x,y) \to (x,y+5)$

So, we have:

$f'(x) = f(x) +5$

$f'(x) = 6x +5$

The rule of reflecting about the y-axis is:

$(x,y) \to (-x,y)$

So, we have:

$g(x) =f(-x)$

$g(x) =6(-x) + 5$

$g(x) =-6x + 5$

Hence, the rule of function g is: $g(x) =-6x + 5$

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