domain and range \( h(x)=\left\{\begin{array}{ll}x^{2}, & -3 \leq x<3 \\ 2-x, & 3 \leq x<7\end{array}\right. \)

For the function \( h(x) \), let's break it down! For the first part, where \( -3 \leq x < 3 \), the output is \( x^2 \), which ranges from \( 0 \) (when \( x = 0 \)) to \( 9 \) (when \( x = 3 \), although 3 is not included). So, the range here is \( [0, 9) \). In the second part, \( 2-x \), where \( 3 \leq x < 7 \), the output goes from \( -1 \) (when \( x = 3 \)) to \( -5 \) (when \( x \) approaches 7). Thus, this segment’s range is \( (-5, -1] \). Combining these, the overall range of \( h(x) \) is \( [0, 9) \cup (-5, -1] \). The domain of \( h(x) \) can be easily identified since it includes all values from \( -3 \) to \( 7 \), taken as \( -3 \leq x < 7 \). Therefore, the domain is simply \( [-3, 7) \). This means you can plug in any x-value from \(-3\) up to, but not including, \(7\), and you'll get a real number output!