What Transformations Change The Graph Of F(X) To The Graph Of G(X) F(X)=x^2 G(X)=(X+7)^2+9

The graph of the function $g(x)=(x+7)^{2}+9$ is obtained from the graph of the function $f(x)=x^{2}$ when each point on the curve of $f(x)=x^{2}$ is shifted $7$ units towards the negative direction of $x-$ axis and then shifted $9$ units towards the positive direction of $y-$ axis.

Further caption:

The functions are given equally follows:

$\fbox{\begin\\\ \begin{aligned}f(x)&=x^{2}\\g(x)&=(x+7)^{2}+9\end{aligned}\\\end{minispace}}$

The objective is to determine the transformation or the style in which the graph of the role $g(x)$ is obtained from the graph of the office $f(x)$ .

Concept used:

Shifting of graphs:

Shifting is a rigid translation because it does not change the size and shape of the bend. Shifting is used to motion the bend vertically or horizontally without any change in shape and size of the curve.

The function $y=f(x+a)$ and $y=f(x-a)$ is a shift of the curve $y=f(x)$ horizontally towards negative and positive management of $x-$ axis respectively.

The function $y=f(x)+a$ and $y=f(x)-a$ is a shift of the curve $y=f(x)$ vertically towards positive and negative direction of $y-$ axis respectively.

Step1: Draw the graph of the function $f(x)=x^{2}$ .

Figure ane (fastened in the end) represents the graph of the role $f(x)=x^{2}$ . From figure 1 it is observed that the curve of the function $f(x)=x^{2}$ is a parabola with origin as the vertex and mounted upwards.

Step 2: Obtain the graph of the function $g'(x)=(x+7)^{2}$ from the graph of the function $f(x)=x2$ .

The office $g'(x)=(x+7)^{2}$ is of the form $y=f(x+a)$ .

So, as per the concept of shifting of the graphs the graph of the function $g'(x)=(x+7)^{2}$ is obtained from the graph of the function $f(x)=x^{2}$ when each point on the curve of $f(x)=x^{2}$ is shifted $7$ units towards the negative direction of $x-$ centrality.

Figure 2 (attached in the cease) represents the graph of the function $g'(x)=(x+7)^{2}$ .

In figure 2 the dotted line represents the curve of $f(x)=x^{2}$ and the bold line represents the curve of $g'(x)=(x+7)^{2}$ .

Step3: Obtain the graph of the function $g(x)=(x+7)^{2}+9$ from the graph of the office $g'(x)=(x+7)^{2}$ .

The function $g(x)=(x+7)^{2}+9$ is of the class $y=f(x)+a$ .

Then, every bit per the concept of shifting of graph the graph of the function $g(x)=(x+7)^{2}+9$ is obtained from the graph of the function $g'(x)=(x+7)^{2}$ when each point on the curve of $g'(x)=(x+7)^{2}$ is shifted $9$ units towards upward or the positive direction of $y-$ centrality.

Effigy iii (fastened in the end) represents the graph of the office $g(x)=(x+7)^{2}+9$ .

In effigy iii the dotted line represents the curve of $g'(x)=(x+7)^{2}$ and the bold line represents the curve of $g(x)=(x+7)^{2}+9$ .

From the above explanation it is concluded that the graph of the function $g(x)=(x+7)^{2}+9$ is obtained from the graph of the function $f(x)=x^{2}$ when each point on the curve of $f(x)=x^{2}$ is shifted $7$ units towards the negative management of $x-$ axis and so shifted $9$ units towards the positive direction of $y-$ axis.

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Answer details:

Class: High school

Subject area: Mathematics

Affiliate: Graphing

Keywords: Graph, curve, role, parabola, quadratic, f(x)=x2, thou(x)=(ten+7)2+9, shifting, translation, scaling, shifting of graph, scaling of graph, horizontal, vertical, coordinate, horizontal shift, vertical shift.