Can you help me understand the table of values function rule y=x^2+(-3) how it works on the table if you can understand what I'm asking thank you
Certainly! The function rule y = x^2 + (-3) represents a quadratic function, where the input value x is squared and then the result is subtracted by 3 to get the output value y.
To understand how this works on a table of values, you can choose input values for x and calculate the corresponding output values for y using the given function. Let's go through an example:
Let's say we have the following inputs for x: -2, -1, 0, 1, 2.
1. For x = -2:
Substituting x = -2 in the function rule, we get:
y = (-2)^2 + (-3) = 4 - 3 = 1
So, when x = -2, y = 1.
2. For x = -1:
Substituting x = -1 in the function rule, we get:
y = (-1)^2 + (-3) = 1 - 3 = -2
So, when x = -1, y = -2.
3. For x = 0:
Substituting x = 0 in the function rule, we get:
y = (0)^2 + (-3) = 0 - 3 = -3
So, when x = 0, y = -3.
4. For x = 1:
Substituting x = 1 in the function rule, we get:
y = (1)^2 + (-3) = 1 - 3 = -2
So, when x = 1, y = -2.
5. For x = 2:
Substituting x = 2 in the function rule, we get:
y = (2)^2 + (-3) = 4 - 3 = 1
So, when x = 2, y = 1.
These pairs of (x, y) values form a table where the x values are the inputs and the y values are the corresponding outputs based on the function rule. Here's how the table would look:
| x | y |
|---|---|
| -2| 1|
| -1| -2|
| 0| -3|
| 1| -2|
| 2| 1|
So, this is how the table of values would look like for the given function rule y = x^2 + (-3).
In the answer you gave me for the table of values explanation what do the parenthesis mean
In the answer I provided, the parentheses "( )" are used to group terms together in the mathematical expression.
Specifically, in the given function rule y = x^2 + (-3), the parentheses around (-3) indicate that the number -3 should be treated as a single term, separate from the x^2 term.
This is useful for clarity, as it explicitly shows that we are subtracting 3 from the x^2 term, rather than combining x^2 and -3 together without clarifying the operation.
So, in this case, the parentheses are used to distinguish the terms in the equation and show that (-3) should be subtracted.
Oh that makes sense thank you
You're welcome! I'm glad it makes sense now. Don't hesitate to ask if you have any more questions. I'm here to help!
Absolutely! I can definitely help you understand how a table of values works for the function rule y = x^2 - 3.
In this function, the expression x^2 represents the square of the input value 'x.' And the term (-3) is subtracted from the squared value.
To create a table of values for this function, we can choose different values of 'x' and compute the corresponding 'y' values.
Let's assume we choose the following values for 'x' -2, -1, 0, 1, and 2. Now, we'll substitute these values into the function rule to find the corresponding 'y' values.
For 'x = -2':
y = (-2)^2 - 3
y = 4 - 3
y = 1
For 'x = -1':
y = (-1)^2 - 3
y = 1 - 3
y = -2
For 'x = 0':
y = (0)^2 - 3
y = 0 - 3
y = -3
For 'x = 1':
y = (1)^2 - 3
y = 1 - 3
y = -2
For 'x = 2':
y = (2)^2 - 3
y = 4 - 3
y = 1
Hence, the table of values for the function rule y = x^2 - 3 is as follows:
x | y
-2 | 1
-1 | -2
0 | -3
1 | -2
2 | 1
Each 'x' value in the left column corresponds to a 'y' value in the right column, according to the function rule.
I hope this explanation helps! If you have any more questions, feel free to ask.
Of course! I can help you understand how the function rule y = x^2 + (-3) works on a table.
To create a table of values for this function, you need to choose several different values for x and substitute them into the equation to find the corresponding y-values.
Let's start by choosing a few values for x. To make it easier, we can choose some simple integers. Let's say we choose x = -2, -1, 0, 1, and 2.
Now let's substitute these values into the equation to find the corresponding y-values. Starting with x = -2:
y = (-2)^2 + (-3)
y = 4 + (-3)
y = 1
For x = -1:
y = (-1)^2 + (-3)
y = 1 + (-3)
y = -2
For x = 0:
y = (0)^2 + (-3)
y = 0 + (-3)
y = -3
For x = 1:
y = (1)^2 + (-3)
y = 1 + (-3)
y = -2
And finally, for x = 2:
y = (2)^2 + (-3)
y = 4 + (-3)
y = 1
Now, to summarize the results in a table:
x | y
------------
-2 | 1
-1 | -2
0 | -3
1 | -2
2 | 1
This table gives you the corresponding y-values for each chosen x-value in the function y = x^2 + (-3). By substituting different values for x, you can generate more pairs of x and y values and observe any patterns or relationships within the function.