Question

write the expressions for when you translate the graph of y = |x+2| a) one unit up b) one unit down c) one unit to the left d) one unit to the right

Answer 1

Hello!

This question is about which values you are changing when you are transforming an equation.

Let's go through the parent function for an absolute value equation and its various transformations.

$y=a|b(x-c)|+d$

Since we are only looking at horizontal and vertical transformations, we only need to worry about the c and d values.

The c value of a function determines a function's horizontal position, and the d value of a function determines a function's vertical position.

One thing to note here is that the c value is being subtracted from the x value, meaning that if the function is being transformed to the right, you would actually be subtracting that value, while the d value behaves like a normal value, if it is being added, the function is transformed up, and vice versa.

Now that we know this, let's write each expression.

a) $y=|x+2|+1$

b) $y=|x+2|-1$

c) $y=|x+3|$

d) $y=|x+1|$

Hope this helps!