(Please) Show all the steps that you use to solve this problem.
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?
To translate any graph to the left 8 units, we replace with x + 8.
giving
f ( x ) = ( x + 8 )²
Now, to shift this graph up 2 units, we addt 2.
getting
g (x) = ( x + 8 )² + 2
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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?
When you see results go on algebra. c o m to see graphs.
Sure, I'll guide you through the steps with a touch of humor, because who said math can't be fun? Let's dive in!
Step 1: Start with the original function, f(x) = x^2.
Step 2: To translate it to the left 8 units, imagine telling the function, "Hey, buddy, I'm moving you to the left, so buckle up!" 🚀
- To shift it to the left, we need to replace x with (x + 8) in the equation.
- Now we have f(x) = (x + 8)^2.
Step 3: Next, we want to move our function up 2 units, like giving it a little boost to help it reach for the stars! 🌟
- To do this, we add 2 to our equation from Step 2.
- Therefore, g(x) = (x + 8)^2 + 2.
And voila! We have successfully translated f(x) to the left 8 units and up 2 units, resulting in our g(x) function rule as g(x) = (x + 8)^2 + 2. 🎉
Remember, math can be as entertaining as a circus—with the added bonus that nobody has to juggle actual knives! If you have any more questions or need further assistance, feel free to ask!
To find the function rule for g(x), which is the translation of f(x), we need to apply the given translations to f(x)=x^2.
1. Translation to the left 8 units:
To translate f(x) to the left 8 units, we replace x with (x + 8).
So, the new function after the left translation is:
f(x) = (x + 8)^2
2. Translation up 2 units:
To translate f(x) up 2 units, we replace f(x) with (f(x) + 2).
So, the final function rule for g(x) after both translations is:
g(x) = (x + 8)^2 + 2
To solve this problem, we need to apply the translation to the function f(x)=x^2. Here are the steps to find the function rule for g(x):
Step 1: Start with the original function f(x)=x^2.
Step 2: To translate the function to the left 8 units, we need to replace x with (x+8).
Step 3: The function after the left translation is f(x+8)=(x+8)^2.
Step 4: Now, to translate the function up 2 units, we need to add 2 to the equation.
Step 5: The function after the up translation is g(x)=f(x+8)+2.
Step 6: Substitute the equation of f(x)=(x+8)^2 into g(x).
Step 7: Simplify the equation, if necessary.
So, the function rule for g(x) is g(x) = (x+8)^2 + 2.