Comparison of Function Values

Oct 13, 2025 by miodeya.com 117 views

In mathematics, functions are used to describe relationships between variables. Evaluating a function at a given value of x involves substituting that value into the function and simplifying the expression. In this article, we will determine the value of each function when x = -4.

Function 1: f(x) = x^2 + 3

To evaluate f(x) at x = -4, we substitute -4 into the function and simplify the expression.

f(-4) = (-4)^2 + 3
f(-4) = 16 + 3
f(-4) = 19

Therefore, the value of f(x) when x = -4 is 19.

Function 2: g(x) = \frac{1}{2} x^2

To evaluate g(x) at x = -4, we substitute -4 into the function and simplify the expression.

g(-4) = \frac{1}{2} (-4)^2
g(-4) = \frac{1}{2} (16)
g(-4) = 8

Therefore, the value of g(x) when x = -4 is 8.

Function 3: h(x) = 3 + x^2

To evaluate h(x) at x = -4, we substitute -4 into the function and simplify the expression.

h(-4) = 3 + (-4)^2
h(-4) = 3 + 16
h(-4) = 19

Therefore, the value of h(x) when x = -4 is 19.

Comparison of Function Values

We have evaluated each function at x = -4 and obtained the following results:

Function	Value at x = -4
f(x) = x^2 + 3	19
g(x) = \frac{1}{2} x^2	8
h(x) = 3 + x^2	19

As we can see, the values of f(x) and h(x) are the same when x = -4, while the value of g(x) is different.

Conclusion

In this article, we have evaluated three functions at x = -4 and determined their values. We have also compared the values of the functions and observed that f(x) and h(x) have the same value, while g(x) has a different value. This demonstrates the importance of evaluating functions at specific values of x to understand their behavior.

Key Takeaways

Evaluating a function at a given value of x involves substituting that value into the function and simplifying the expression.
The value of a function at a given value of x can be used to understand the behavior of the function.
Different functions can have the same or different values at a given value of x.

Conclusion

In this article, we have answered some frequently asked questions about evaluating functions at a given value of x. We have discussed how to evaluate functions at a given value of x, how to handle functions with variables in the denominator, how to handle functions with square roots, and how to handle functions with complex numbers. We have also discussed how to determine if a function is defined at a given value of x and how to handle functions with vector input values.

Key Takeaways

Evaluating a function at a given value of x involves substituting that value into the function and simplifying the expression.
The value of a function at a given value of x can be used to understand the behavior of the function.
Different functions can have the same or different values at a given value of x.
Functions are typically defined for scalar input values, not vector input values.