Question

Which equation represents the transformation formed by horizontally shifting the graph of f(x)=√ 6 units to the right and then

vertically shrinking the graph by a factor of ?
g(x)=√2z+6
g(2)=√2-6
g(2)=√2+6
g(z)= 2√2-6

Answer 1

The equation that represents the transformation of the graph of f(x) = √6 units to the right and then vertically shrinking the graph by a factor of 1/2 is g(x) = √(2x + 6)/2.

The transformation of the graph of f(x) = √6 units to the right and then vertically shrinking the graph by a factor of 1/2 can be represented by the equation g(x) = √(2x + 6)/2.

Here's how we know this:

The horizontal shift to the right can be represented by the term "x" in the new function g(x). This means the graph is shifted 6 units to the right.

The vertical shrinking by a factor of 1/2 can be represented by the term "1/2" inside the square root in the new function g(x). This means the graph is stretched vertically by a factor of 1/2.

So, the equation that represents the transformation of the graph of f(x) = √6 units to the right and then vertically shrinking the graph by a factor of 1/2 is g(x) = √(2x + 6)/2.