107k views
2 votes
Help please 1. Describe the transformations necessary to transform the graph of

f(x) to that of g(x)
f(x) = x² and g(x) = 3(x - 1)² + 4

User Toji
by
8.6k points

1 Answer

2 votes

Here are all the steps, and what they do:

STEP 1: HORIZONTAL TRANSLATION

We transform


x^2\mapsto (x-1)^2

The general transformation is


f(x)\mapsto f(x+k)

These transformations translate the graph horizontally, k units to the left if k>0, k units to the right if k<0.

In this case, k = -1, so we translate the original graph 1 unit to the right.

STEP 2: VERTICAL STRETCH

We transform


(x-1)^2\mapsto 3(x-1)^2

The general transformation is


f(x)\mapsto kf(x)

These transformations stretch the graph vertically. The graph expands if |k|>1, while it shrinks if 0<|k|<1. If k is negative, we also reflect the graph with respect to the x axis.

In this case, k = 3, so we stretch the graph vertically by a factor 3.

STEP 3: VERTICAL TRANSLATION

We transform


3(x-1)^2\mapsto 3(x-1)^2+4

The general transformation is


f(x)\mapsto f(x)+k

These transformations translate the graph vertically, k units up if k>0, k units down if k<0.

In this case, k = 4, so we translate the graph 4 units up.

So, we start from the original graph of
f(x)=x^2 and we:

  • Translate it 1 unit to the right
  • Stretch it vertically by a factor 3
  • Translate it 4 units up

(the order is important!)

to get the graph of
g(x)=3(x-1)^2+4

User Christian Vielma
by
8.5k points

No related questions found

Welcome to QAmmunity.org, where you can ask questions and receive answers from other members of our community.

9.4m questions

12.2m answers

Categories