Question

Write a g rule for g that represents a translation 2 units down, followed by the reflection in the x-axis of the graph of f(x)=2^x

Answer 1

The answer to this question is g(x) = - 2^x + 2. You first translate it down
                               g(x) = 2^(x) - 2
Then you reflect it in the x-axis by multiplying everything by a negative, which results in
                               g(x) = -(2^(x) - 2) = -2^(x) + 2

Answer 2

$g(x)=x^2-2$

What is the meaning of translate down a unit?

To translate the point P(x,y) , a units left and b units down, use P'(x−a,y−b) .

What is reflection on x axis?

The rule for reflecting over the X axis is to negate the value of the y-coordinate of each point, but leave the x-value the same.

Given:

$f(x)=x^2\\\\\text{Translating 2 units down, }\\\\g(x)=f(x)-2=x^2-2\\\\\text{On reflecting on x axis,}\\\\g(x)=x^2-2$

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