for f(x)= squareroot x
to h(x)= f(-3x-12)
sketch thegraph....
when i did this i did
h(x)= f(-3(x+4))
you know the negitve 3 isit reflection on the x ais or the y axis... thank you!!!
To sketch the graph of h(x) = f(-3x-12), where f(x) = √x, you need to understand the transformations applied to the original function f(x).
Let's break it down step by step:
1. Start with the parent function f(x) = √x, which is the square root function.
2. Apply the transformation -3x to f(x), which horizontally stretches the graph by a factor of 3 in the x-direction. This means that every x-coordinate in f(x) will now be one-third of its original value.
3. Apply the transformation -3x-12 to the result of the previous step. This horizontally shifts the entire graph 12 units to the right. So, every x-coordinate in the function -3x will now be 12 units greater.
Therefore, h(x) = f(-3x-12) represents a horizontally stretched and shifted version of f(x).
Next, let's address the confusion about reflection. In this case, there is no reflection involved. The negative sign in front of 3 (-3x) indicates the stretching in the horizontal direction and has nothing to do with reflecting the graph.
To sketch the graph, follow these steps:
1. Plot a few key points of the parent function f(x) = √x. For example, (0,0), (1,1), (4,2), etc.
2. Apply the transformations to these key points. Multiply each x-coordinate by -1/3 to account for the horizontal stretching, and then shift each x-coordinate 12 units to the right.
3. Connect the transformed points to form the graph of h(x) = f(-3x-12).
Remember, the graph of the function will start at the transformed x-intercept and continue upward from there.
I hope this explanation helps you understand how to sketch the graph of h(x) = f(-3x-12). Let me know if you have any further questions!