What Transformations Change The Graph Of F(X) To The Graph Of G(X)? F(X) = X2 G(X) = (X 5)2- 9

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

Farther caption:

The functions are given as 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 fashion in which the graph of the function $g(x)$ is obtained from the graph of the function $f(x)$ .

Concept used:

Shifting of graphs:

Shifting is a rigid translation because it does non alter the size and shape of the curve. Shifting is used to move 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 direction of $x-$ axis respectively.

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

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

Figure 1 (fastened in the cease) represents the graph of the function $f(x)=x^{2}$ . From figure 1 it is observed that the bend of the part $f(x)=x^{2}$ 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 function $g'(x)=(x+7)^{2}$ is of the form $y=f(x+a)$ .

So, every bit 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 part $f(x)=x^{2}$ when each point on the bend of $f(x)=x^{2}$ is shifted $7$ units towards the negative direction of $x-$ axis.

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

In figure two 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 office $g(x)=(x+7)^{2}+9$ from the graph of the office $g'(x)=(x+7)^{2}$ .

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

So, as 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 part $g'(x)=(x+7)^{2}$ when each point on the curve of $g'(x)=(x+7)^{2}$ is shifted $9$ units towards upwards or the positive management of $y-$ axis.

Figure 3 (attached in the end) represents the graph of the part $g(x)=(x+7)^{2}+9$ .

In figure 3 the dotted line represents the curve of $g'(x)=(x+7)^{2}$ and the assuming line represents the curve of $g(x)=(x+7)^{2}+9$ .

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

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Reply details:

Grade: Loftier school

Subject: Mathematics

Chapter: Graphing

Keywords: Graph, curve, office, parabola, quadratic, f(x)=x2, g(x)=(10+7)2+9, shifting, translation, scaling, shifting of graph, scaling of graph, horizontal, vertical, coordinate, horizontal shift, vertical shift.