Determining the Values of x

Oct 13, 2025 by talynt.org 105 views

Understanding the Problem

The problem presents us with the graphs of two functions, f and g, and asks us to determine the age of each function at specific points. This requires us to analyze the graphs and understand the behavior of the functions at different values of x.

(a) Which is Older, f(0) or g(0)?

To determine which function is older at x = 0, we need to look at the point where the graphs intersect the y-axis. The y-axis represents the value of the function at x = 0.

Analyzing the Graphs: Looking at the graph, we can see that the function f intersects the y-axis at a point above the x-axis, while the function g intersects the y-axis at a point below the x-axis.
Determining the Age: Since the function f is above the x-axis at x = 0, it means that f(0) is positive. On the other hand, since the function g is below the x-axis at x = 0, it means that g(0) is negative. Therefore, f(0) is older than g(0).

(b) Which is Older, f(23) or g(23)?

To determine which function is older at x = 23, we need to look at the point where the graphs intersect the line x = 23.

Analyzing the Graphs: Looking at the graph, we can see that the function f intersects the line x = 23 at a point above the x-axis, while the function g intersects the line x = 23 at a point below the x-axis.
Determining the Age: Since the function f is above the x-axis at x = 23, it means that f(23) is positive. On the other hand, since the function g is below the x-axis at x = 23, it means that g(23) is negative. Therefore, f(23) is older than g(23).

(c) For Which Values of x is f(x) = g(x)?

To determine the values of x for which f(x) = g(x), we need to find the points where the graphs intersect.

Analyzing the Graphs: Looking at the graph, we can see that the graphs intersect at two points: one point above the x-axis and one point below the x-axis.
Determining the Values of x: Since the graphs intersect at two points, it means that f(x) = g(x) at these two points. To find the values of x, we need to look at the x-coordinates of the intersection points. The x-coordinates of the intersection points are 0 and 23.

Conclusion

In conclusion, we have determined that f(0) is older than g(0), f(23) is older than g(23), and f(x) = g(x) at x = 0 and x = 23.

Key Takeaways

The age of a function at a specific point can be determined by analyzing the graph of the function.
The y-axis represents the value of the function at x = 0.
The line x = 23 represents the value of the function at x = 23.
The graphs of two functions intersect at points where the functions have the same value.

Final Thoughts

The problem requires us to analyze the graphs of two functions and determine the age of each function at specific points. This requires us to understand the behavior of the functions at different values of x and to analyze the graphs to determine the values of x for which f(x) = g(x).

Understanding the Problem

Q&A

Q: What is the age of f(0) compared to g(0)?

A: The age of f(0) is older than g(0) because f(0) is positive, while g(0) is negative.

Q: What is the age of f(23) compared to g(23)?

A: The age of f(23) is older than g(23) because f(23) is positive, while g(23) is negative.

Q: For which values of x is f(x) = g(x)?

A: f(x) = g(x) at x = 0 and x = 23.

Q: How can we determine the age of a function at a specific point?

A: We can determine the age of a function at a specific point by analyzing the graph of the function. The y-axis represents the value of the function at x = 0, and the line x = 23 represents the value of the function at x = 23.

Q: What is the significance of the intersection points of the graphs?

A: The intersection points of the graphs represent the values of x for which f(x) = g(x).

Q: How can we use the graphs to determine the values of x for which f(x) = g(x)?

A: We can use the graphs to determine the values of x for which f(x) = g(x) by looking at the x-coordinates of the intersection points.

Key Takeaways

The age of a function at a specific point can be determined by analyzing the graph of the function.
The y-axis represents the value of the function at x = 0.
The line x = 23 represents the value of the function at x = 23.
The graphs of two functions intersect at points where the functions have the same value.

Final Thoughts

Common Mistakes to Avoid

Not analyzing the graphs carefully to determine the age of the functions.
Not understanding the significance of the intersection points of the graphs.
Not using the graphs to determine the values of x for which f(x) = g(x).

Tips for Success

Carefully analyze the graphs to determine the age of the functions.
Understand the significance of the intersection points of the graphs.
Use the graphs to determine the values of x for which f(x) = g(x).

Conclusion

In conclusion, we have determined the age of f(0) and f(23) compared to g(0) and g(23), and we have found the values of x for which f(x) = g(x). We have also provided tips for success and common mistakes to avoid.