Math problems

Question

Write the equation of a function which has the same shape as f(x)=(square root of)x but which vertically stretched by 3, reflected across the y axis and shifted up two units.

 

I kinda have the gist of this problem but am unsure. Please explain your thinking. Please note that I could not find a radical sign, hence why I put "square root of x" in parenthesis.

Thanks for the help!

Answer 1

You begin with a function f(x)

 

you stretch it vertically by a factor of three  g(x) = 3f(x)

 

You reflect it across the y- axis  h(x) = -g(x)  

 

You shift it up by 2, k(x) = h(x) + 2

 

k(x) = -g(x) + 2

k(x) = -3f(x) + 2

 

and f(x) was the square root function 

 

k(x) = 2 -3√x      terms reversed for clarity without parentheses