Question

Which equation represents the transformation formed by vertically stretching the graph of f(x)=√ by a factor of 6 and then

vertically shifting the graph 7 units up?
O g(x) = √6x + 7
O g(x)=6√x+7
○ g(x)=√x+7
O g(x)=√√√x+7

Answer 1

(b) g(x) = 6√x +7

Explanation:

You want the equation of the square root function after it has been vertically stretched by a factor of 6 and translated up 7 units.

Stretch

A vertical stretch is accomplished by multiplying the function value by 'a', where 'a' is the vertical stretch factor. That means the stretched square root function will be ...

f(x) = √x . . . . original square root function

h(x) = 6·f(x) = 6√x . . . . . vertically stretched by a factor of 6

Translation

A translation upward is accomplished by adding the translation amount to the function value. The translated function will be ...

h(x) . . . . . original function

g(x) = h(x) +7 . . . . . translation upward by 7 units

Our stretched and translated function is ...

g(x) = 6√x +7