The graph of the function
is obtained from the graph of the function
when each point on the curve of
is shifted
units towards the negative direction of
axis and then shifted
units towards the positive direction of
axis.
Further explanation:
The functions are given as follows:
![\fbox{\begin\\\ \begin{aligned}f(x)&=x^{2}\\g(x)&=(x+7)^{2}+9\end{aligned}\\\end{minispace}}](https://tex.z-dn.net/?f=%5Cfbox%7B%5Cbegin%5C%5C%5C%20%5Cbegin%7Baligned%7Df%28x%29%26%3Dx%5E%7B2%7D%5C%5Cg%28x%29%26%3D%28x%2B7%29%5E%7B2%7D%2B9%5Cend%7Baligned%7D%5C%5C%5Cend%7Bminispace%7D%7D)
The objective is to determine the transformation or the way in which the graph of the function
is obtained from the graph of the function
.
Concept used:
Shifting of graphs:
Shifting is a rigid translation because it does not change the size and shape of the curve. Shifting is used to move the curve vertically or horizontally without any change in shape and size of the curve.
The function
and
is a shift of the curve
horizontally towards negative and positive direction of
axis respectively.
The function
and
is a shift of the curve
vertically towards positive and negative direction of
axis respectively.
Step1: Draw the graph of the function
.
Figure 1 (attached in the end) represents the graph of the function
. From figure 1 it is observed that the curve of the function
is a parabola with origin as the vertex and mounted upwards.
Step 2: Obtain the graph of the function
from the graph of the function
.
The function
is of the form
.
So, as per the concept of shifting of the graphs the graph of the function
is obtained from the graph of the function
when each point on the curve of
is shifted
units towards the negative direction of
axis.
Figure 2 (attached in the end) represents the graph of the function
.
In figure 2 the dotted line represents the curve of
and the bold line represents the curve of
.
Step3: Obtain the graph of the function
from the graph of the function
.
The function
is of the form
.
So, as per the concept of shifting of graph the graph of the function
is obtained from the graph of the function
when each point on the curve of
is shifted
units towards upwards or the positive direction of
axis.
Figure 3 (attached in the end) represents the graph of the function
.
In figure 3 the dotted line represents the curve of
and the bold line represents the curve of
.
From the above explanation it is concluded that the graph of the function
is obtained from the graph of the function
when each point on the curve of
is shifted
units towards the negative direction of
axis and then shifted
units towards the positive direction of
axis.
Learn more:
1. A problem to determine the equation of line brainly.com/question/1646698
2. A problem on ray brainly.com/question/1251787
3. A problem to determine intercepts of a line brainly.com/question/1332667
Answer details:
Grade: High school
Subject: Mathematics
Chapter: Graphing
Keywords: Graph, curve, function, parabola, quadratic, f(x)=x2, g(x)=(x+7)2+9, shifting, translation, scaling, shifting of graph, scaling of graph, horizontal, vertical, coordinate, horizontal shift, vertical shift.