Question

How to create an equation for function m? I wrote the right equation as a guess, but I don't understand it.​

Answer 1

Answer:

$h(x)=2(x + 3)^{\frac{1}{2} }$

Step-by-step explanation:

Parent function of the square root function has been given as,

f(x) = $x^{\frac{1}{2} }$

If the graph of the given function is stretched vertically by the scale factor = g(x) = $k(x^\frac{1}{2})$

If the graph is shifted 3 units to the left,

h(x) = $k(x + 3)^{\frac{1}{2} }$

Since, the graph of the function passes through a point (-2, 2),

$2=k(-2 + 3)^\frac{1}{2}$

2 = k

Therefore, the function is $h(x)=2(x + 3)^{\frac{1}{2} }$.