Chapter 9, Problem 1MCQ

To determine

Use a table of values to graph each equation. State the domain and range.

Answer to Problem 1MCQ

The domain is all real numbers. The range is all real numbers greater than or equal to the minimum value or $\{y|y\ge \frac{5}{4}\}$

Explanation of Solution

Given:

The equation: $y=x^2+3x+1$

Concept Used:

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 which will make the function "work", and will output real y-values. 

The range of a function is the complete set of all possible resulting values of the dependent variable ( y,  usually), after we have substituted the domain.

Calculation:

Make table to get some points on the graph

x	$y=x^2+3x+1$	(x, y)
0	$y=0^2+3·0+1=1$	(0, 1)
−1	$y={(-1)}^2+3·-1+1=1-3+1=-1$	(− 1 , − 1 )
−2	$y={(-2)}^2+3·-2+1=4-6+1=-1$	(− 2 , − 1)
−4	$y={(-4)}^2+3·-4+1=16-12+1=5$	( − 4 , − 5 )
1	$y={(1)}^2+3·1+1=1+3+1=5$	( 1, 5 )

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 $\{y|y\ge \frac{5}{4}\}$

Thus, the domain is all real numbers. The range is all real numbers greater than or equal to the minimum value or $\{y|y\ge \frac{5}{4}\}$