Answer:
The modified function has a translation of 3 units to the right and 4 units up compared to the parent function.
Step-by-step explanation:
Let's change both functions to y.
How does y = (x - 3)^3 + 4 compare with the parent function y = x^3?
Start with y = (x - 3)^3 + 4 and subtract 4 from both sides.
y - 4= (x - 3)^3
Now compare the function above with the parent function below.
y = x^3
We notice two differences. y of the parent function becomes y - 4 in the modified function. x of the parent function becomes x - 3 in the modified function.
When you replace x by x - h, the function is translated h units horizontally. The translation is to the right if h is positive and to the left if h is negative.
When you replace y by y - k, the function is translated k units vertically. The translation is up if k is positive and down if k is negative.
In the modified function, x became x - 3.
Compare x - 3 with x - h.
h = 3
3 is positive, so the modified function was translated 3 units to the right.
In the modified function, y becomes y - 4.
Compare y - 4 with y - k.
k = 4
4 is positive, so the modified function is translated 4 units up.
Answer:
The modified function has a translation of 3 units to the right and 4 units up compared to the parent function.
