Question

Determine whether the equation defines y as a function of $x$.

$y=2x^2-3x+4$

Short answer

The given equation is a function.

Step-by-step solution

Step 1. Given information

In the given question we have to determine whether the equation defines y as a function of x.

$y=2x^2-3x+4$

Step 2. The given equation is y=2x2-3x+4

The equation tells us to take an input $x$and find their square.

For any input $x$, these operations yield only one output $y$.

Step 3. For example, 

If $x=1$, then

role="math" localid="1645889500415" $$\begin{gathered} y=2{\left(1\right)}^2-3\times 1+4 \\ y=2-3+4 \\ y=3 \end{gathered}$$.

If $x=2$, then

role="math" localid="1645889543035" $$\begin{gathered} y=2{\left(2\right)}^2-3\times 2+4 \\ y=2\times 4-6+4 \\ y=8-6+4 \\ y=6 \end{gathered}$$.

For this reason, the equation is a function.