F(x)={4x-2 if x is less than or equal to 2, x squared+2 if x is greater than 2}

[tex] f(x)\left \{ {4x-2, x\leq2} \atop {x^2+2,x>2}} \right.

In the interval (-∞, 2], the graph will represent the linear function f(x) = 4x - 2.

In the interval (2, ∞), the graph will represent the exponential function f(x) = x² + 2.

for this case we must apply distributive property to the following expression:

the distributive property states that:

then, when applying the property we have to multiply the -2 for each term within the parenthesis:

the absolute value function