What will happen to the given function if a graph is shifted 2 units left and 3 units up?(2 points)

Question

f(x)=x3
will become g(x)=
( x+

)3+

Answer 1

To shift the graph of the function \( f(x) = x^3 \) 2 units to the left and 3 units up, we need to adjust the function accordingly.

1. Shift left by 2 units: When shifting a function to the left by \( a \) units, we replace \( x \) with \( x + a \). Here, we shift left by 2 units, so: \[ f(x) \to f(x + 2) = (x + 2)^3 \]

2. Shift up by 3 units: When shifting a function up by \( b \) units, we add \( b \) to the function. Here, we shift up by 3 units, so: \[ f(x + 2) \to f(x + 2) + 3 = (x + 2)^3 + 3 \]

Putting it all together, the new function \( g(x) \) will be: \[ g(x) = (x + 2)^3 + 3 \]

So, filling in the blanks, the expression for \( g(x) \) is: \[ g(x) = (x + 2)^3 + 3 \]