What are the domain, range, and asymptote of \( h(x)=(0.5)^{x}-9 \) ? domain: \( \{x \mid x>-9\} ; \) range: \( \{y \mid y \) is a real number \( \} \); asymptote: \( y=-9 \) domain: \( \{x \mid x \) is a real number \( \} \); range: \( \{y \mid y>9\} \); asymptote: \( y=9 \) domain: \( \{x \mid x \) is a real number\}; range: \( \{y \mid y>-9\} ; \) asymptote: \( y=-9 \)

For the function \( h(x) = (0.5)^x - 9 \): 1. **Domain**: - The function \( (0.5)^x \) is defined for all real numbers \( x \). - Therefore, the domain of \( h(x) \) is: \[ \{ x \mid x \text{ is a real number} \} \] 2. **Range**: - The exponential function \( (0.5)^x \) is always positive and approaches 0 as \( x \) approaches infinity. - Subtracting 9 shifts the entire graph down by 9 units. - Thus, \( h(x) \) will always be greater than \( -9 \): \[ \{ y \mid y > -9 \} \] 3. **Asymptote**: - As \( x \) approaches infinity, \( (0.5)^x \) approaches 0. - Therefore, the horizontal asymptote is: \[ y = -9 \] **Final Answer**: - **Domain**: All real numbers. - **Range**: All real numbers greater than –9. - **Asymptote**: \( y = -9 \). In symbols: • Domain: { x | x is a real number } • Range: { y | y > −9 } • Asymptote: y = −9