Question

The parent function of h(x) = |x+5| -2 I need to find out the parent equation and then put both equations into Desmos Graph Calculator, and then we need to figure out the transformations

Answer 1

ANSWER:

f(x) = |x|

Translation: 5 units left and 2 units down

STEP-BY-STEP EXPLANATION:

The parent function is the simplest function that still satisfies the definition of a given type of function. For example, when we think of the linear functions that make up a family of functions, the parent function would be y = x. This is the simplest linear function.

We have the following function:

$h\mleft(x\mright)=|x+5|-2$

Therefore, the parent function will be:

$f(x)=|x|$

Graph both functions and we are left with the following:

Therefore, the transformation splits into two translations, one that is 5 units to the left and the other that is 2 units down.