Describing Transformations

[nycmathguy]

Section 1.7
Question 22

In Exercises 21–38, g is related to one of the parent functions.

(a) Identify the parent function f.

(b) Describe the sequence of transformations from f to g.

(c) Sketch the graph of g.

(d) Use function notation to write g in terms of f.

I will show my effort here. Apply correction where needed.

22. g(x) = x^2 − 2

Let me see.

Part (a)

The parent function is f(x) = x^2.

Part (b)

The parent function was shifted down two units. Yes?

Part (c)

I will do this on paper as a last step.

Part (d)

I'm not sure if this is right but here we go. I found the parent function to be f(x) = x^2. I need to write g in terms of f.

Let me see.

g(x) = x^2 - 2

We know that f(x) = x^2. I think it's just a basic substitution.

My answer is g(x) = f(x) - 2.

You say?

I will do a few more examples after a reply to this question.

 

[MathLover1]

all correct

 

[nycmathguy]

all correct

Feels good to be right.