Rewrite the function to make it easy to graph using transformations of its parent function. Describe the transformations of the graph. y=8x−24−−−−−−√3+1

Answer 1

To make the function easy to graph using transformations of its parent function, we can rewrite it in the form:

y = a√(bx - h) + k

Given function: y = 8x - 24 - √3 + 1

First, simplify the function:
y = 8x - 23 - √3

Now, we can rewrite the function in the desired form by factoring out a constant from the x term:
y = √1(8(x - 23/8)) - √3

The transformed function with the following transformations:
a = 1
b = 8
h = 23/8
k = -√3

Transformations of the graph:
- Vertical shift down by √3 units
- Horizontal compression by a factor of 1/b = 1/8
- Horizontal shift right by h units (23/8)
- No vertical stretch or reflection

By transforming the function in this way, it will be easier to graph using transformations of its parent function.