A graph G is obtained from a graph of y by the following sequence of transformations. Write an equation whose graph is G.
y=|x|: a shift left 9 units, then a vertical stretch by a factor of 7, and finally a shift down 6 units
Thank you so much!!!
y=|x|
a shift left 9 units ---> y = |x+9|
then a vertical stretch by a factor of 7 ----> y = 7|x+9|
and finally a shift down 6 units -----> y= 7|x+9| + 6
check:
http://www.wolframalpha.com/input/?i=plot+y+%3D+%7Cx%7C+,+y+%3D+%7Cx%2B9%7C,+y+%3D+7%7Cx%2B9%7C,y%3D+7%7Cx%2B9%7C+%2B+6
Thank you!
To obtain the equation whose graph is G, we need to apply the given transformations to the equation y = |x|.
1. Shift left 9 units: Subtract 9 from x.
New equation: y = |x - 9|
2. Vertical stretch by a factor of 7: Multiply the entire equation by 7.
New equation: 7y = 7|x - 9|
3. Shift down 6 units: Subtract 6 from y.
New equation: 7y - 6 = 7|x - 9|
Therefore, the equation whose graph is G is 7y - 6 = 7|x - 9|.
To obtain the equation of the graph G, which is obtained by transforming the graph of y=|x|, we need to perform each transformation in reverse order.
First, we need to shift the graph left 9 units. In general, to shift a graph horizontally, you add or subtract the desired amount inside the function. In this case, a left shift of 9 units is equivalent to replacing "x" in the equation with "(x+9)".
So, the new equation after the left shift is: y=|x+9|
Next, we need to apply a vertical stretch by a factor of 7. To vertically stretch a graph, you multiply the entire function by the desired factor. Thus, multiplying y=|x+9| by 7 gives us: y=7|x+9|
Finally, we need to shift the graph down 6 units. Similarly, to shift a graph vertically, you add or subtract the desired amount outside the function. A downward shift of 6 units can be achieved by replacing "y" in the equation with "(y-6)".
So, after the downward shift, the final equation of the graph G is: (y-6)=7|x+9|
This equation represents the graph G, which is obtained by shifting the graph of y=|x| left 9 units, vertically stretching it by a factor of 7, and then shifting it down 6 units.