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Algebra
Question

2. Find the domain and range of each function. Explain your answers.

a) $$f ( x ) = - 2 ( x + 3 ) ^ { 2 } + 5$$                  c) $$f ( x ) = 3 x - 4$$

b) $$f ( x ) = 2 x ^ { 2 } + 4 x + 7$$                        d) $$x = 5$$

2)

a)

Domain of $$- 2 ( x + 3 ) ^ { 2 } + 5$$ : $$\left[ \begin{array} { c c } {$$ Solution: $$} & { - \infty < x < \infty } \\ {$$ Interval Notation: $$} & { ( - \infty , \infty ) } \end{array} \right]$$

Range of $$- 2 ( x + 3 ) ^ { 2 } + 5$$ : $$\left[ \begin{array} { c l } {$$ Solution: $$} & { f ( x ) \leq 5 } \\ {$$ Interval Notation: $$} & { ( - \infty , 5 ] } \end{array} \right]$$

b)

Domain of $$2 x ^ { 2 } + 4 x + 7$$ $$\left[ \begin{array} { c c } {$$ Solution: $$} & { - \infty < x < \infty } \\ {$$ Interval Notation: $$} & { ( - \infty , \infty ) } \end{array} \right]$$

Range of $$2 x ^ { 2 } + 4 x + 7$$ $$\left[ \begin{array} { c c } {$$ Solution: $$} & { f ( x ) \geq 5 } \\ {$$ Interval Notation: $$} & { [ 5 , \infty ) } \end{array} \right]$$

c)

Domain of $$3 x - 4 :$$ $$\left[ \begin{array} { c c } {$$ Solution: $$} & { - \infty < x < \infty } \\ {$$ Interval Notation: $$} & { ( - \infty , \infty ) } \end{array} \right]$$

Range of $$3 x - 4$$ : $$\left[ \begin{array} { c c } {$$ Solution: $$} & { - \infty < f ( x ) < \infty } \\ {$$ Interval Notation: $$} & { ( - \infty , \infty ) } \end{array} \right]$$

d)

Solution
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