Question

The functions f(x) and g(x) are shown on the graph.F(x)=x^2What is g(x)?A. g(x)= -x^2+3B. g(x)=(-x)^2-3C. g(x)=(-x)^2+3D.g(x)= -x^2-3

Answer 1

On observation of the graphs of the two functions, we can see that f(x) has undergone some transformation to give g(x).

The original function is given as

$f(x)=x^2$

The function is reflected over the x-axis.

The rule for the reflection over the x-axis is given as

$f(x)\to-f(x)$

Applying this to the function, we have the new function to be

$-x^2$

The graph is also shifted downwards by 3 units.

This shift can be represented as

$f(x)\to f(x)-3$

Applying this to our function, we have the new function, g(x), to be

$g(x)=-x^2-3$

The correct option is OPTION D.