Question

which statement best describes the function below?
$f(x) = 2x^2 - 3x + 1$
a. it is not a function.
b. it fails the vertical line test.
c. it is a many - to - one function.
d. it is a one - to - one function.

Explanation:

Step1: Verify if it's a function

A relation where each x has one y is a function. For $f(x)=2x^2-3x+1$, every input $x$ gives exactly one output, so it is a function.

Step2: Check vertical line test

A function passes the vertical line test (no vertical line intersects its graph more than once). This quadratic's graph is a parabola, which passes the test.

Step3: Classify function type

A one-to-one function passes the horizontal line test. For $f(x)=2x^2-3x+1$, a horizontal line will intersect the parabola at two points (e.g., $f(0)=1$ and $f(\frac{3}{2})=1$). Thus, it is many-to-one.

Answer:

C. It is a many-to-one function.