Question

Use a table of values to graph the following functions. State the domain and range.

$\mathit{y}\mathbf{=}\mathbf{2}{\mathit{x}}^{\mathbf{2}}\mathbf{-}\mathbf{3}\mathit{x}\mathbf{+}\mathbf{1}$

Short answer

The graph of the function is:

The domain is all real numbers and the range is $\left\{y|y\ge -\frac{1}{8}\right\}$.

Step-by-step solution

Step 1. Define the concept.

The domain of a function is the complete set of possible values of the independent variable. The domain is the set of all possible $x$-values that will make the function "work" and will output real $y$-values.

Therangeof a function is the complete set of all possibleresulting valuesof the dependent variable ($y$,usually) after we have substituted the domain.

Step 2. Make a table to calculate points on the graph. 

For the equation, ,make a table to get some points on the graph.

$x$	$y=2x^2-3x+1$	$(x,y)$
$–1$	$y=0^2-4\left(0\right)+3=3$	$(-1,3)$
0	$y=2{\left(0\right)}^2-3\left(0\right)+1=1$	$(0,1)$
1	$y=2{\left(1\right)}^2-3\left(1\right)+1=0$	role="math" localid="1648204828518" $(1,0)$
$1.5$	$y=2{\left(1.5\right)}^2-3\left(1.5\right)+1=1$	$(1.5,1)$

Graph the ordered pairs, and connect them to create a smooth curve. The parabola extends to infinity.

Step 3. Graph the equation and write domain and range.

Graph the ordered pairs, and connect them to create a smooth curve. The parabola extends to infinity.

The domain is all real numbers. The range is all real numbers greater than or equal to the minimum value or $\left\{y|y\ge -\frac{{\displaystyle 1}}{{\displaystyle 8}}\right\}$.