Find the function gx ax b whose graph can be obtained by tr

Find the function g(x) = ax +b whose graph can be obtained by translating the graph of f(x) = 2x +5 up 2 units and to the left 3 units?

f(x) = 2x + 5

Assume h(x) is function when moved up by 2 units

h(x) = f(x) + 2

h(x) = 2x+5+2 = 2x+7

Assume g(x) is function when h(x) is moved left 3 units

g(x) = h(x-(-3)) = h(x+3)

g(x) = 2(x+3) + 7

g(x) = 2x+6+7

g(x) = 2x + 13

So in g(x) = ax + b, a = 2, b = 13