Concept explainers
(a)
Define the function
(a)
Answer to Problem 12SGR
The function
Explanation of Solution
Given:
The function
Concept Used:
If the coefficient of
If the coefficient of
The graph of any quadratic function is a parabola.
Thus, the function
(b)
State the maximum or minimum value
(b)
Answer to Problem 12SGR
Maximum value is at x = 1.5
Explanation of Solution
Given: The function
Concept Used:
If the coefficient of
If the coefficient of
The graph of any quadratic function is a parabola.
Calculation: The graph of the function
Thus, the graph has maximum value is at x = 1.5
(c)
Find the domain and range of the function.
(c)
Answer to Problem 12SGR
The domain is all real numbers. The range is all real numbers greater than or equal to the maximum value or
Explanation of Solution
Given: The function:
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.
Thus, the domain is all real numbers. The range is all real numbers greater than or equal to the maximum value or
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Algebra 1
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