Question Find the ordered pairs $(x, y)$ that satisfy the equation $f(x) = x^2 - 9 = y$ .

Studdy Solution

STEP 1

Assumptions
1. The function given is $f(x) = x^2 - 9$ .
2. The table provides values of $x$ and corresponding $y$ values, where $y = f(x)$ .
3. We need to identify the ordered pairs that are solutions to the function.

STEP 2

To find the ordered pairs, we need to plug in the $x$ values into the function $f(x)$ and verify if the corresponding $y$ values match the output of the function.

STEP 3

Start with the first ordered pair where $x = -3$ . Plug $x = -3$ into the function $f(x)$ .
$f(-3) = (-3)^2 - 9$

STEP 4

Calculate the value of $f(-3)$ .
$f(-3) = 9 - 9$

STEP 5

Simplify the result to find $y$ .
$f(-3) = 0$

STEP 6

The ordered pair for $x = -3$ is $(-3, 0)$ . This matches the second value in the table, confirming that it is a correct solution.

STEP 7

Now, we need to find the second ordered pair. We are given the $y$ value of 0 and need to find the corresponding $x$ value.

STEP 8

Set the function equal to 0 and solve for $x$ .
$x^2 - 9 = 0$

STEP 9

Add 9 to both sides of the equation to isolate $x^2$ .
$x^2 = 9$

STEP 10

Take the square root of both sides to solve for $x$ .
$x = \pm\sqrt{9}$

STEP 11

Calculate the square root of 9.
$x = \pm3$

STEP 12

We have two possible $x$ values, $x = 3$ and $x = -3$ . Since we already used $x = -3$ for the first ordered pair, the second ordered pair must be $x = 3$ .

STEP 13

The ordered pair for $x = 3$ is $(3, 0)$ . This matches the last value in the table, confirming that it is a correct solution.

STEP 14

The identified ordered pairs of the solutions are $(-3, 0)$ and $(3, 0)$ .
The solutions are: $(-3, 0) ;(3, 0)$

Was this helpful?

Get Studdy

Scan QR code with your device to get Studdy on iOS or Android

QR code

Studdy solves anything!

Download the app

Start learning now

Download Studdy AI Tutor now. Learn with ease and get all help you need to be successful at school.

Parents Influencer program Contact Policy Terms