Please help
the graph of g(x) is f(x) translated to the left 8 units and up 2 units what is the function rule for g(x) given f(x)=x^2.
Can someone explain this to me.
The I have a graph that has the top corner shaded the point is on 1 going off the side and the other line is going to an angle up to 6 on the y axis is there anyway you might be able to help write an inequality.it looks kinda like the inequality y<=[x+3]+1 except oppisite sides of graph and different numbers
f(x-h) is the graph of f(x) translated to the right by h units.
So, you have g(x) = f(x+8)
g(x)-k = f(x) is the graph translated up k units
So, now you have
g(x)-2 = f(x+8)
or
g(x) = f(x-8) + 2
g(x) = (x-8)^2 + 2
As for the inequality, it's a bit murky. What does "the point is on 1" mean? Give us some coordinates, how they are connected, and which region is shaded. "Top corner" doesn't pin it down enough.
oops g(x) = (x+8)^2 + 2
To find the function rule for g(x) given f(x) = x^2, which is a translation of f(x) to the left 8 units and up 2 units, you need to apply the appropriate transformations to the original function.
1. Translation to the left: When a function is translated to the left by 'a' units, you subtract 'a' from the x-coordinate of each point on the graph.
In this case, since f(x) is translated to the left by 8 units, the new function g(x) will have the x-coordinate of each point decreased by 8.
2. Translation up: When a function is translated up by 'b' units, you add 'b' to the y-coordinate of each point on the graph.
In this case, since f(x) is translated up by 2 units, the new function g(x) will have the y-coordinate of each point increased by 2.
So, to obtain the function rule for g(x), we subtract 8 from x and add 2 to y in the function rule for f(x), which is f(x) = x^2.
Therefore, the function rule for g(x) is g(x) = (x-8)^2 + 2.
Now, moving on to the second part of your question about writing an inequality to match the given graph:
Based on your description, the graph looks like a shaded region that has one side going along the x-axis and the other side slanting upwards (positive slope).
To write an inequality for this graph, we can start with the inequality y ≤ (x + 3) + 1, but we need to make some modifications:
1. Opposite sides of the graph: Since you mentioned that the graph has opposite sides shaded, it means we need to reverse the inequality sign for one side.
Since the original inequality has ≤ (less than or equal to), we can change it to ≥ (greater than or equal to) for the other side.
2. Different numbers: We need to adjust the numbers in the inequality to match the specific graph.
Without knowing the exact details, we can modify the inequality as follows:
y ≤ -(x - 3) + 1
In this inequality, the left side represents the y-values, and the right side represents the corresponding x-values in the shaded region.
Remember, this modified inequality is based on the information you provided about the graph's appearance. If you have more specific information or the actual graph, the inequality can be adjusted accordingly.