Question

How would you solve this question:
What kind of transformation converts the graph of f(x) = -9|x + 8| - 4 into the graph of g(x) = -9|x + 8| - 2?

Answer 1

An absolute value function has the generic formula
\[f(x) = a \left| x-h \right| + k\]
Where:
-"a" defines how steep the graph is and in which direction it opens it.
-"k" is the axis of symmetry of the graph
-"(h, k)" is the vertex of the graph

The only thing that changes in the two functions you gave is the "k" value, which determines the axis of symmetry. The axis of symmetry goes from -4 to -2, and the graph stays the same in every other way.

The moving of a graph or other representation on a coordinate plane is called a translation. When specifying a translation, the direction and number of units must be given. If the x-coordinate gets higher, the graph must move towards the right. Since -4 - (-2) = 2, the graph will move a total of two units.

The name of the transformation would be a translation two units to the right.

Hope I helped clear things up :) Let me know if you have any more questions!

Answer 2

Awesome thanks! I knew the answer was two units to the right but I didn't know how exactly to explain that.

Answer 3

Today I took a quiz with the same question. It turned out that the answer was a translation two units up. Why? @Sionainn

Answer 4

I messed it up... so sorry :( For some reason I thought that the "k" in (h, k) was the x-coordinate, so I thought it moved to the right. In reality, "k" is the y-coordinate, and since it increased, the graph moved up. Sorry about my mistake :(

Answer 5

@Sionainn Lol its fine. I fell into the same mistake! So h is x and k is y, correct? And thanks for the help!

Answer 6

Yep, "h" represents the x-coordinate (remember, it's inverted in the formula) and "k" represents the y-coordinate

Answer 7

@Sionainn Alright. Thanks again!