When the graph of f(x) is translated five units up, the function g(x) becomes g(x) = 3x + 5.
Given function is , f(x) = 3x
We can get,
f(1) = 3(1) =3
f(2) = 3(2) = 6
f(3) = 3(3) = 9
f(0) = 3(0) = 0
f(-1) = 3(-1) = -3
f(-2) = 3(-2) = -6
x 1 2 3 0 -1 -2
f(x) 3 6 9 0 -3 -6
Let us assume, new function is g(x)
Think about the parent function f. (x),
If you want to scale a function up or down by a certain amount, let g(x) = f(x) + b.
Your graph is translated upward if b is positive and downward if b is negative.
Let g(x) Equal f(x + a) when moving a function to the right or left by a certain amount (let's say a).
Your graph will be translated to the left if an is positive and to the right if an is negative.
As a result, when the graph of the function f(c) = 3x is translated 5 units upward, the function g(x) will be as follows:
g(x) = f(x) + 5 (because 5 units up)
We can substitute f(x) value,
g(x) = 3x + 5
Therefore,
The function g(x) when the graph of f(x) is translated 5 units up is g(x) = 3x + 5.
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