Question

Given the parent function f(x) - xdescribe the graph of y = (x - 5)2 - 2.

a. translated right 2 units and down 5 units c. translated left 5 units and down 2 units
b. translated right 5 units and down 2 units
translated left 2 units and down 2 units

Answer 1

b. translated right 5 units and down 2 units

Explanation:

Assuming the parent function is:

f(x) = x²

f(x) = (x - 5)² is obtained by translating the graph 5 units towards right

f(x) = (x - 5)² - 2 is obtained by again translating the graph 2 units down

Answer 2

translated right 5 units and down 2 units

Explanation:

Horizontal transformations are those that only alter the x, while vertical transformations are those that alter the entire function.

Here, the -5 is only changing the x, so we know that it must be a horizontal transformation of some sort. It turns out that this is actually a horizontal translation 5 units either to the right or left. We know that it is a translation to the right because it uses a "-" sign instead of "+" (this is because horizontal transformations are "backward" and a little weird like that). So, the graph of y is translated 5 units to the right.

Now, look at the -2 at the end of the function. Because it isn't solely in the parentheses with the x, we know that -2 is changing the entire function and is thus a vertical transformation. It's actually a vertical translation 2 units either up or down. We know that it's a translation down because of the "-" sign. Unlike horizontal transformations, vertical transformations are "correct", so "+" means up and "-" means down. So the graph of y is translated 2 units down.

Hope this helps!