Given the parent function, write the equation of the new function after a translation of 5 units up

Question



Answer 1

Functions in the same family are transformations of their parent function. A translation is a transformation that shifts a graph horizontally and or vertically but does not change its size, shape or orientation.

so if a parent function is Y = aX + b

then the new function after translation of 5 units up should be Y = aX + b + 5

note: a (slope) should not be changed.

Answer 2

Were you given a specific parent function? All of the parent functions follow the same or a very similar template. I’ll use a quadratic equation as an example first.

Parent function: y = x²

The template for this function is: y = a (x - h)² + k

1. a represents the vertical stretch or shrink - it’s kind of like slope
2. h represents the graph shifting left or right. It uses the opposite sign, so up is minus and down is plus.
3. k represents the graph shifting down or up. It uses the same sign, so down is minus and up is plus.

In your problem, the k needs to be changed to show 5 units up. You would want to replace k with + 5.

y = a (x - h)² + k

y = a (x - h)² + 5

Since there is no a or h values given because the graph doesn’t change that way, you can get rid of them from the template, so your answer is y = x² + 5.

It works the same way with absolute value as another example.

Parent function: y = |x|

Template: y = a |x - h| + k

Your answer: y = |x| + 5

I hope this helps! If you need a last minute tutoring session, please reach out to me!