Sure! Let's go through this step-by-step.
We are given the function:
[tex]\[ f(x) = 7x - 18 \][/tex]
We need to find the ordered pair [tex]\((x, y)\)[/tex] that corresponds to the equation [tex]\(f(x) = 3\)[/tex].
### Step 1: Set up the equation
Given [tex]\(f(x) = 3\)[/tex], we substitute into the function:
[tex]\[ 7x - 18 = 3 \][/tex]
### Step 2: Solve for [tex]\(x\)[/tex]
Add 18 to both sides of the equation to isolate the term with [tex]\(x\)[/tex]:
[tex]\[ 7x - 18 + 18 = 3 + 18 \][/tex]
[tex]\[ 7x = 21 \][/tex]
Now, divide both sides by 7 to solve for [tex]\(x\)[/tex]:
[tex]\[ x = \frac{21}{7} \][/tex]
[tex]\[ x = 3 \][/tex]
### Step 3: Determine the corresponding [tex]\(y\)[/tex] value
In this case, we already know that [tex]\(f(x) = 3\)[/tex], so:
[tex]\[ y = 3 \][/tex]
### Step 4: Combine [tex]\(x\)[/tex] and [tex]\(y\)[/tex] into an ordered pair
The ordered pair [tex]\((x, y)\)[/tex] is:
[tex]\[ (x, y) = (3, 3) \][/tex]
### Conclusion
Therefore, the ordered pair that corresponds to the equation [tex]\(f(x) = 3\)[/tex] is:
[tex]\[ (3, 3) \][/tex]
### Range of the Relation
Since the function [tex]\(f(x) = 7x - 18\)[/tex] is a linear function, the range is all real numbers [tex]\((-\infty, \infty)\)[/tex].
So the ordered pair for the equation [tex]\(f(x) = 3\)[/tex] is:
[tex]\[ (3, 3) \][/tex]
And the range of the function is:
[tex]\[ (-\infty, \infty) \][/tex]
