Understanding the Function and the Problem

Oct 13, 2025 by miodeya.com 12 views

Understanding the Function and the Problem

The given function is $f(x) = x + 4$ . This is a simple linear function where the output is the input value plus 4. The problem asks us to find the ordered pair for the point on the graph where $x = 3p$ . This means we need to substitute $x$ with $3p$ in the function and find the corresponding value of $f(x)$ .

Substituting $x$ with $3p$ in the Function

To find the ordered pair, we need to substitute $x$ with $3p$ in the function $f(x) = x + 4$ . This gives us:

$f(3p) = 3p + 4$

Finding the Ordered Pair

The ordered pair for a point on the graph is in the form $(x, f(x))$ . In this case, we have $x = 3p$ and $f(x) = 3p + 4$ . Therefore, the ordered pair is:

$(3p, 3p + 4)$

Comparing with the Options

Let's compare the ordered pair we found with the options given:

A. ${$ (x, x+4)$}$ B. ${$ (x, 3p+4)$}$ C. ${$ (3p, 3p+4)$}$ D. ${$ (3p, x+4)$}$

The only option that matches our ordered pair is:

C. ${$ (3p, 3p+4)$}$

Conclusion

Therefore, the correct answer is option C. The ordered pair for the point on the graph where $x = 3p$ is $(3p, 3p + 4)$ .

Understanding the Graph of the Function

The graph of the function $f(x) = x + 4$ is a straight line with a slope of 1 and a y-intercept of 4. The point $(3p, 3p + 4)$ lies on this line. To visualize the graph, we can plot several points on the line and connect them with a straight line.

Plotting Points on the Graph

Let's plot several points on the graph of the function $f(x) = x + 4$ . We can choose several values of $x$ and find the corresponding values of $f(x)$ .

$x$	$f(x)$
0	4
1	5
2	6
3	7
4	8

We can plot these points on a coordinate plane and connect them with a straight line. The point $(3p, 3p + 4)$ lies on this line.

Visualizing the Graph

The graph of the function $f(x) = x + 4$ is a straight line with a slope of 1 and a y-intercept of 4. The point $(3p, 3p + 4)$ lies on this line. We can visualize the graph by plotting several points on the line and connecting them with a straight line.

Conclusion

In conclusion, the ordered pair for the point on the graph where $x = 3p$ is $(3p, 3p + 4)$ . This point lies on the graph of the function $f(x) = x + 4$ , which is a straight line with a slope of 1 and a y-intercept of 4.

Frequently Asked Questions

Q: What is the function $f(x) = x + 4$ ?

A: The function $f(x) = x + 4$ is a simple linear function where the output is the input value plus 4.

Q: What is the ordered pair for the point on the graph where $x = 3p$ ?

A: The ordered pair for the point on the graph where $x = 3p$ is $(3p, 3p + 4)$ .

Q: How do I visualize the graph of the function $f(x) = x + 4$ ?

A: You can visualize the graph of the function $f(x) = x + 4$ by plotting several points on the line and connecting them with a straight line.

Q: What is the slope of the graph of the function $f(x) = x + 4$ ?

A: The slope of the graph of the function $f(x) = x + 4$ is 1.

Q: What is the y-intercept of the graph of the function $f(x) = x + 4$ ?

A: The y-intercept of the graph of the function $f(x) = x + 4$ is 4.

Q: How do I find the ordered pair for a given function?

A: To find the ordered pair for a given function, you need to substitute the value of $x$ into the function and find the corresponding value of $f(x)$ .

Q: What is the difference between the ordered pair and the function?

A: The ordered pair is a point on the graph of the function, while the function is the equation that describes the relationship between the input and output values.

Q: Can I use the function $f(x) = x + 4$ to find the value of $x$ ?

A: Yes, you can use the function $f(x) = x + 4$ to find the value of $x$ by rearranging the equation to solve for $x$ .

Q: How do I rearrange the equation to solve for $x$ ?

A: To rearrange the equation to solve for $x$ , you need to isolate $x$ on one side of the equation.

Example: Rearranging the Equation to Solve for $x$

Let's say we have the equation $f(x) = x + 4$ and we want to find the value of $x$ when $f(x) = 7$ . We can rearrange the equation to solve for $x$ as follows:

$f(x) = x + 4$ $7 = x + 4$ $x = 7 - 4$ $x = 3$

Therefore, the value of $x$ is 3.

Conclusion

In conclusion, the function $f(x) = x + 4$ is a simple linear function where the output is the input value plus 4. The ordered pair for the point on the graph where $x = 3p$ is $(3p, 3p + 4)$ . We can visualize the graph of the function by plotting several points on the line and connecting them with a straight line. The slope of the graph is 1 and the y-intercept is 4. We can use the function to find the value of $x$ by rearranging the equation to solve for $x$ .