The function f(x)=x-9 is shifted 2 units up and 3 units to the left. what is the new function

f(x) = (x + 3) - 7

Step-by-step explanation:

the original function f(x) = x - 9 is the parent function f(x) = x shifted down 9 units

from f(x) = x - 9, we are told that the function is shifted 2 units up, this is a vertical shift. so we add 2 to -9

-9 + 2 = -7

we now have f(x) = x - 7

next we are told that the function is shifted 3 units to the left. this is a horizontal shift. a horizontal shift looks similar to this:

f(x) = (x ± b)

if a function is shifted to the left, we would use an addition sign. if it was going to the right, we would use a subtraction sign

the function looks like the following when we apply the above knowledge

f(x) = (x + 3) - 7 this would be our new function

.25

step-by-step explanation: