The function f(x)=x^2. The graph of g(x) is f(x) translated to the right 3 units and down 3 units. What is the function rule for g(x)?
I honestly have no idea how to this… An example or helping me get through the problem would be great :) Thank you so much :)
to move up or down just add or subtract the constant equal to the units moved
so just to move it DOWN 3 would give us
g(x) = x^2 - 3
to move horizontally replace each x with (x ± c)
if you move it to the right, you need x - c
if you move it to the left , you need x + c
so , since we are moving 3 units to the right, we replace the x with x-3
g(x) = (x-3)^2 - 3
This should be in your notes or in your text.
Well, well, well, we've got ourselves a translation party here! Don't worry, I've got your back. Let's break it down step by step.
First, we're dealing with the function f(x) = x^2. If we want to translate it to the right 3 units, we need to replace x with (x - 3). So now we'd have (x - 3)^2.
Next, if we want to bring it down 3 units, we subtract 3 from the whole function. So we end up with (x - 3)^2 - 3.
And there you have it! The function rule for g(x) is g(x) = (x - 3)^2 - 3. Voila! Now go out there and rock those translations!
Sure! Let's break down the problem step by step.
1. Start with the original function f(x) = x^2. This is a quadratic function that represents a parabola with its vertex at the origin (0,0).
2. To translate the function to the right 3 units, we need to subtract 3 from the x-coordinate of each point on the graph. This means that the function will now be defined as f(x - 3).
3. To translate the function down 3 units, we need to subtract 3 from the y-coordinate of each point on the graph. Since the original function is f(x), translating it down 3 units will result in g(x) = f(x) - 3.
4. Putting it all together, the function rule for g(x) is g(x) = (x - 3)^2 - 3.
So, the graph of g(x) is the graph of the function f(x), translated 3 units to the right and 3 units down.
I hope this helps! Let me know if you have any further questions.
Sure! Let's break down the problem step by step.
We start with the function f(x) = x^2.
To translate the graph of f(x) to the right 3 units, we need to subtract 3 from the x-coordinate. So, each input value (x) needs to be decreased by 3.
To translate the graph of f(x) down 3 units, we need to subtract 3 from the output values (y or f(x)). So, each output value (y or f(x)) needs to be decreased by 3.
Combining both translations, the rule for g(x) can be derived as follows:
g(x) = f(x - 3) - 3
This means we first shift the x-coordinate 3 units to the right by subtracting 3 from x, then evaluate the function f(x) at the new x-coordinate, and finally, subtract 3 from the result.
Now, if you substitute f(x) = x^2 into the rule for g(x), we can simplify it further:
g(x) = (x - 3)^2 - 3
So, the function rule for g(x) is g(x) = (x - 3)^2 - 3.
Hope this helps! Let me know if there's anything else I can do for you.