Answer:
Step-by-step explanation:
We have to solve the given expression,
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Answer:
Dilation followed by Translation.
Step-by-step explanation:
We have the function .
The new transformed function is
Now, the transformation applied to f(x) to obtain g(x) are:
1. Dilation - it is the transformation that changes the size/shape of the figure. It is generally of the form kf(x) where k is constant.
Since, we are dilating the given function by 2 units, the new dilated function becomes .
2. Translation - it is the transformation that shifts the figure in any direction. When the function is shifted vertically, the general form becomes f(x)+k.
As, we see that the new dilated function is shifted 3 units upwards, the final translated function becomes .
Hence, the transformations applied to obtain g(x) from f(x) are Dilation followed by Translation.
Explanation:
The function is
To graph the function, let us find the x and y intercepts.
To find x-intercept, let us substitute y=0 in the function
Thus, the x-intercept is
To find the y-intercept, let us substitute x=0, we get,
Thus, the y-intercept is
The graph has no asymptotes.
To plot the points in the graph, we need to substitute the values for x in the function , to find the y-values.
The points are . The image of the graph and table is attached below:
