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

y=2x23x+1

Short Answer

Expert verified

The graph of the function is:

The domain is all real numbers and the range is {y|y18}.

Step by step solution

01

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.

02

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=2x23x+1

(x,y)

1

y=024(0)+3=3

(1,3)

0

y=2(0)23(0)+1=1

(0,1)

1

y=2(1)23(1)+1=0

role="math" localid="1648204828518" (1,0)

1.5

y=2(1.5)23(1.5)+1=1

(1.5,1)

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

03

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 y|y18.

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