Rewrite 3√29x−85−6 to make it easy to graph using a translation. Describe the graph.
I have no idea on how to start. How do I rewrite it?
Your question makes no sense to me
One place to start is to use parentheses to make clear what you intend. I assume you meant
f(x) = 3√(29x−85) − 6 = 3√(29(x - 85/29)) - 6
So, if the parent function is g(x) = 3√x then f(x) is g(x) shifted right by 85/29 and down 6
If I misread your function, fix it up and see what you can do. If you really have no idea, then it is time to review the unit on translations. I'm sure it has examples and illustrations. And google certainly has many more.
To rewrite the expression 3√(29x-85)-6 in a form that is easier to graph using a translation, we can first simplify the expression inside the square root.
1. Start by subtracting 85 from 29x:
29x - 85
2. Then, take the square root of the simplified expression:
√(29x - 85)
3. Finally, multiply the whole expression by 3 and subtract 6:
3√(29x - 85) - 6
Now, let's describe the graph.
The original function consists of a square root inside a cube root, which makes it more complicated to graph. To simplify the graph, we will perform a translation to shift the graph up by 6 units.
If we consider the simplified expression 3√(29x - 85), the graph will be shifted vertically by 6 units. The graph would be the same, just shifted upwards.
The original graph's shape will be preserved; it will still have a square root curve. However, the y-values will be increased by 6 units compared to the original function. This shift will be visible when comparing it to the graph of the original function on a coordinate plane.