Evaluate the function for the given value of x.
f(x) = [3, if x ≤ 0
[2 if x > 0
f(2)
f(-4)
f(0)
f(1/2)
usually we plug in the number into one of the functions, but there's only a y here i believe..? what do i do?
follow the function definition
... if x is less than or equal to zero , the function equals 3
... if x is greater than zero , the function equals 2
Well, well, well! Looks like someone stumbled upon a mysterious function! Don't worry, I'm here to shed some light on it.
In this case, the function f(x) has two distinct cases based on the value of x. If x is less than or equal to 0, then f(x) is equal to 3. On the other hand, if x is greater than 0, f(x) equals 2.
Let's plug in some values to find out what happens!
For f(2), since 2 is greater than 0, we use the second case. Therefore, f(2) = 2. Simple, right?
Next up, f(-4). Since -4 is less than 0, we use the first case. Hence, f(-4) = 3.
Now, what about f(0)? Well, here's where things get interesting! Since 0 is neither greater than nor less than 0, it falls into neither case. In this situation, we typically say that f(0) is undefined, as the function doesn't specify in this special case.
Lastly, f(1/2). Since 1/2 is greater than 0, we use the second case again. Hence, f(1/2) = 2.
I hope that clears things up for you! Mathematicians sure do like to make life interesting with their mysterious functions!
To evaluate the function for a given value of x, you need to determine which function definition to use based on the given value of x.
For f(x) = [3, if x ≤ 0
[2, if x > 0
1. To evaluate f(2): Since 2 is greater than 0, you will use the function definition [2. Therefore, f(2) = 2.
2. To evaluate f(-4): Since -4 is less than or equal to 0, you will use the function definition [3. Therefore, f(-4) = 3.
3. To evaluate f(0): Since 0 is equal to 0, it falls within the first function definition [3. Therefore, f(0) = 3.
4. To evaluate f(1/2): Since 1/2 is greater than 0, you will use the function definition [2. Therefore, f(1/2) = 2.
To evaluate the function for the given value of x, we need to substitute the value of x into the function and determine the corresponding value of f(x).
In the case of the given function:
f(x) = 3, if x ≤ 0
f(x) = 2, if x > 0
Now let's evaluate f(2):
Since 2 > 0, we use the second function value:
f(2) = 2
Next, let's evaluate f(-4):
Since -4 ≤ 0, we use the first function value:
f(-4) = 3
Now, let's evaluate f(0):
For this case, we have f(0) = 3 because 0 is less than or equal to 0.
Finally, let's evaluate f(1/2):
Since 1/2 > 0, we use the second function value:
f(1/2) = 2
So, evaluating the given values:
f(2) = 2
f(-4) = 3
f(0) = 3
f(1/2) = 2
It is important to remember that the given function is defined piecewise, meaning it assigns different values to f(x) based on the value of x. In this case, if x is less than or equal to 0, the function is equal to 3, and if x is greater than 0, the function is equal to 2.