Question

The graphs below have the same shape. Complete the equation of the blue

Answer 1

Answer:

the answer is G(x)=x^2 + 1

1. if you add +1, the y value will increase 1 point upward making the other function equal to g(x)=x^2 + 1. the difference between the two functions is the + 1.

Answer 2

Answer:

$g(x)=(x+3)^{2}+1$

Step-by-step explanation:

In the image, we have two functions, the red one is a parent function, which is the most basic version of it. The blue function is a transformation of the red one, that is, it was only moved to the left and upwards.

So, to find the equation for $g(x)$ we just have to apply the right operations which give the transformation,

If we sum or subtract units to $f(x)$ we can move the function upwards or downwards.

If we sum or subtract units to $x$ we can move the function to the left or right.

So, we observe that the blue function was moved to the left and upwards, that means we have to sum units to $x$ and $f(x)$:

$g(x)=(x+3)^{2}+1$

If we sum units to $x$, the curve will move to the left.

If we sum units to $f(x)$, the curve will move upwards.

You can observe in the graph that the blue curve was moved three units to the left and one unit upwards.

Therefore, the expression is: $g(x)=(x+3)^{2}+1$