Compare the function with the parent function without graphing what are the avertex axis of symmetry and transformation of the given function.

Y=l8x-2l-7

parent: y = |x|

new function. graph is
shifted right by 1
dilated by a factor of 1/4
shifted down by 7
because |8x-2| - 7 = |4(x-1)| - 7
new axis: x = 1/4

see the graphs at

www.wolframalpha.com/input/?i=plot+y%3D%7Cx%7C%2C+y%3D+%7C8x-2%7C+-+7

Well, well, well! Looks like we have a funky function here. Let's dive right into it!

The given function is Y = |8x-2| - 7. We can compare it to the parent function Y = |x|.

Firstly, let's talk about the vertex. In the parent function, the vertex is at (0, 0). However, in our given function, the vertex is affected by the transformation. To find the vertex, we need to set the inside of the absolute value equal to zero and solve for x.

8x - 2 = 0
8x = 2
x = 2/8
x = 1/4

So, the vertex of our given function is located at (1/4, -7).

Next up, we have the axis of symmetry. In the parent function, the axis of symmetry is the y-axis, represented as x = 0. For our given function, since the vertex is shifted to the right (positive x-value), the axis of symmetry is shifted accordingly. Therefore, the axis of symmetry for our given function is x = 1/4.

Lastly, let's discuss the transformation. The absolute value function has no transformation except for reflecting the negative values. So, in our given function, the transformation is a horizontal translation to the right by 1/4 units.

To sum it up:
- Vertex: (1/4, -7)
- Axis of Symmetry: x = 1/4
- Transformation: Horizontal translation to the right by 1/4 units

Hope that puts a smile on your face! Let me know if you need any more fun facts or if there's anything else I can assist you with!

To compare a given function with its parent function without graphing, we need to identify the changes in the equation.

The parent function is the basic form of a function, which in this case would be the absolute value function, f(x) = |x|.

Comparing the given function, Y = l8x-2l-7, with the parent function, we can identify the following changes:

1. The coefficient before x, which is 8 in this case, indicates a vertical stretch or compression. However, since it is outside the absolute value function, it affects the amplitude rather than the shape of the graph.

2. The -2 inside the absolute value function causes a horizontal shift. It shifts the graph to the right if it is positive or to the left if it is negative.

3. The -7 at the end of the equation shifts the entire graph vertically. It moves the graph downwards by 7 units if positive or upwards by 7 units if negative.

Now, let's determine the vertex, axis of symmetry, and the transformation of the given function:

Vertex:
To find the vertex, we can find the x-value that results in the minimum or maximum value of the function. For an absolute value function in the form Y = a | x - h | + k, the vertex is (h, k).
In this case, we have Y = l8x-2l-7. The vertex is when 8x-2 equals zero since the absolute value function will always be positive. So, 8x-2 = 0. Solving for x, we have x = 2/8 = 1/4. Substituting x = 1/4 into the equation, we can find the y-value of the vertex:
Y = l8(1/4)-2l-7 = l2-2l-7 = l-3l-7 = 3-7 = -4.

Therefore, the vertex of the given function is (1/4, -4).

Axis of Symmetry:
The axis of symmetry is the vertical line that passes through the vertex. In this case, the axis of symmetry is the vertical line x = 1/4.

Transformation:
The transformations of the given function can be summarized as follows:
- Vertical stretch or compression depending on the coefficient before x (8 in this case).
- Horizontal shift to the right by 2 units due to the -2 inside the absolute value function.
- Vertical shift downwards by 7 units due to the -7 at the end of the equation.

In conclusion, the vertex of the given function is (1/4, -4), the axis of symmetry is x = 1/4, and the transformations include a vertical stretch or compression, a horizontal shift to the right, and a vertical shift downwards.

To compare the given function, y = l8x - 2l - 7, with the parent function, we need to identify the vertex, axis of symmetry, and any transformations applied to the parent function y = lxl.

The parent function y = lxl is a simple V-shaped absolute value function with the vertex at the origin (0, 0).

To find the vertex of the given function, we need to set the expression inside the absolute value, 8x - 2, equal to 0 and solve for x:
8x - 2 = 0
8x = 2
x = 2/8
x = 1/4

So, the vertex of the given function is at (1/4, ...).

The axis of symmetry for an absolute value function is the vertical line passing through its vertex. In this case, the axis of symmetry is x = 1/4.

To identify the transformation, we need to compare the given function with the parent function y = lxl. The given function has a coefficient of 8 multiplied with x and has a constant term of -7 subtracted, which are both transformations.

The coefficient of 8 horizontally stretches the graph compared to the parent function. Generally, if the coefficient of x is greater than 1, the graph is horizontally compressed, and if it is less than 1, the graph is horizontally stretched. In this case, since the coefficient is 8, the function is horizontally stretched.

The constant term of -7 shifts the graph vertically downwards by 7 units compared to the parent function. A negative constant shifts the graph downwards, and a positive constant shifts it upwards.

So, to summarize:
- The vertex of the given function is (1/4, ...).
- The axis of symmetry is x = 1/4.
- The function has a horizontal stretch with a coefficient of 8.
- The function is vertically shifted downwards by 7 units.