Question

Let the graph of $g$ be a translation 2 units up, followed by a reflection in the $x$ -axis and a vertical stretch by a factor of 6 of the graph of $f(x)=x^2$ . Identify the rule for $g$ .

Answer 1

The rule for g is g(x) = -6x^2 - 2.

Step-by-step explanation:

To identify the rule for the function g, which is a translation 2 units up, followed by a reflection in the x-axis and a vertical stretch by a factor of 6 of the graph of f(x) = x^2, we need to apply each transformation step by step.

Step 1: Translation 2 units up: g(x) = f(x) + 2

Step 2: Reflection in the x-axis: g(x) = -f(x) - 2

Step 3: Vertical stretch by a factor of 6: g(x) = -6f(x) - 2

Therefore, the rule for g is g(x) = -6x^2 - 2.