Question

identify the domain and range for the following function: $f(x) = -2x + 5$
range choose...
domain choose...

Explanation:

Step1: Analyze the function type

The function \( f(x) = -2x + 5 \) is a linear function, which is a polynomial function of degree 1. For polynomial functions, there are no restrictions on the input values (x - values) because we can plug in any real number for \( x \) and get a valid output. So, the domain of a linear function is all real numbers.

Step2: Determine the range

A linear function with a non - zero slope (\( m=-2
eq0 \)) is a straight line that extends infinitely in both the positive and negative y - directions. For any real number \( y \), we can solve the equation \( y=-2x + 5 \) for \( x \): \( x=\frac{5 - y}{2} \). Since for every real number \( y \), we can find a corresponding real number \( x \), the range of the linear function \( f(x)=-2x + 5 \) is also all real numbers.

Answer:

• Domain: All real numbers (or in interval notation \( (-\infty,\infty) \))
• Range: All real numbers (or in interval notation \( (-\infty,\infty) \))