The function `f(x) = x^(2) - 3x + 7` is an example of

Options

A. Identity function
B. Constant function
C. Polynomial function
D. Modulus function

Answer

To determine the type of function represented by \( f(x) = x^2 - 3x + 7 \), we can analyze its characteristics step by step.

### Step 1: Identify the form of the function
The given function is \( f(x) = x^2 - 3x + 7 \). This is a quadratic expression in the standard form \( ax^2 + bx + c \), where \( a = 1 \), \( b = -3 \), and \( c = 7 \).

**Hint:** Look for the highest power of \( x \) in the function to determine its degree.

### Step 2: Determine the degree of the function
The highest power of \( x \) in the function is 2 (from \( x^2 \)). Therefore, the degree of the function is 2.

**Hint:** The degree of a polynomial function is determined by the highest exponent of the variable.

### Step 3: Classify the function based on its degree
Since the degree of the function is greater than 1 and it is a polynomial expression, we can classify it as a polynomial function.

**Hint:** A polynomial function is defined as a function that can be expressed in the form \( a_n x^n + a_{n-1} x^{n-1} + ... + a_1 x + a_0 \), where \( n \) is a non-negative integer.

### Step 4: Check if it's a constant function or identity function
- A constant function returns the same value for any input \( x \), which is not the case here since \( f(x) \) changes with different values of \( x \).
- An identity function returns the input value itself, which also does not apply here since \( f(x) \) does not equal \( x \) for all \( x \).

**Hint:** A constant function will have no \( x \) terms, and an identity function will have the form \( f(x) = x \).

### Conclusion
Thus, the function \( f(x) = x^2 - 3x + 7 \) is classified as a **polynomial function**.

**Final Answer:** The function \( f(x) = x^2 - 3x + 7 \) is an example of a polynomial function.