Compare the function with the parent function. What are the vertex, axis of symmetry, and transformations of the given function? y = |10x-2| -7
(1/5,-7); x=1/5; translated to the right 1/5 unit and down 7 units.
It wouldn’t be up 7 units because the 7 is negative so therefore you’re going down
Nope. Just a question from my algebra work that Im stuck on. Im in algebra 2
y = |10x-2|-7 = |10(x - 1/5)|-7
so, the graph has been shifted right 1/5, compressed horizontally by a factor of 1/10, and then shifted down 7.
Or, since you can also write it as
y = 10|x - 1/5|-7
you could say it has been stretched vertically by a factor of 10 and then down.
I need help same question different problem y=6x-2-7
Ashley I hope you’re right
To compare the given function, y = |10x-2| - 7, to the parent function, y = |x|, we need to determine the vertex, axis of symmetry, and any transformations applied to the parent function to obtain the given function.
1. Vertex: The vertex of the parent function, y = |x|, is at the origin (0,0). To find the vertex of the given function, we need to determine the values of x and y that will make the expression inside the absolute value, 10x-2, equal to zero.
Setting 10x-2 = 0 and solving for x, we get:
10x = 2
x = 2/10
x = 1/5
Plugging this value of x into the given function, we find:
y = |10(1/5) - 2| - 7
y = |10/5 - 2| - 7
y = |2 - 2| - 7
y = 0 - 7
y = -7
Therefore, the vertex of the given function is (1/5, -7).
2. Axis of Symmetry: For the parent function, y = |x|, the axis of symmetry is the y-axis (x = 0). However, when we apply transformations to the function, the axis of symmetry may shift.
Since the graph of the given function is symmetrical about the vertex, the axis of symmetry remains the same. Therefore, the axis of symmetry for the given function is x = 1/5.
3. Transformations: Comparing the given function, y = |10x-2| - 7, to the parent function, y = |x|, we can identify the following transformations:
a. Vertical Shift: The term -7 in the given function causes a vertical shift downward by 7 units compared to the parent function. This means the graph is shifted 7 units down.
b. Stretch/Compression: The coefficient 10 in front of the x causes a horizontal compression/stretch. It stretches the graph horizontally by a factor of 1/10 compared to the parent function. This means the graph becomes narrower.
c. Horizontal Shift: The constant term -2 inside the absolute value causes a horizontal shift rightward by 2/10 units compared to the parent function. This means the graph is shifted 2/10 units to the right.
To summarize the transformations:
- There is a vertical shift downward by 7 units.
- There is a horizontal compression/stretch by a factor of 1/10.
- There is a horizontal shift rightward by 2/10 units.
Therefore, the vertex of the given function is (1/5, -7), the axis of symmetry is x = 1/5, and the transformations include a vertical shift downward by 7 units, a horizontal compression/stretch by a factor of 1/10, and a horizontal shift rightward by 2/10 units.
So what is the axis of symmetry and the vertex?
the axis of symmetry is where
x - 1/5 = 0 or in other words x = 1/5
Look, the absolute value sign means it is the same both right and left of here.
Now find y at x = 1/5 and you have your vertex