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) \( x = 5\)
Question
Answer
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)