What are the domain, range, and asymptote of \( h(x)=(1.4)^{x}+5 \) ? domain: \( \{x \mid x \) is a real number \( \} \); range: \( \{y \mid y>5\} \); asymptote: \( y=5 \) domain: \( \{x \mid x>5\} \); range: \( \{y \mid y \) is a real number \( \} \); asymptote: \( y=5 \) domain: \( \{x \mid x>-5\} \); range: \( \{y \mid y \) is a real number \( \} \); asymptote: \( y=-5 \) domain: \( \{x \mid x \) is a real number \( \} \); range: \( \{y \mid y>-5\} \); asymptote: \( y=-5 \)

Let's analyze the function \( h(x) = (1.4)^x + 5 \): 1. **Domain**: - Exponential functions of the form \( a^x \) are defined for all real numbers \( x \). - Therefore, the domain of \( h(x) \) is all real numbers. 2. **Range**: - The base \( 1.4 \) is greater than 1, so \( (1.4)^x \) is always positive. - Adding 5 shifts the entire graph upward by 5 units. - Thus, the smallest value \( h(x) \) can approach is just above 5. - Therefore, the range of \( h(x) \) is \( y > 5 \). 3. **Asymptote**: - The horizontal asymptote of an exponential function \( a^x + k \) is \( y = k \). - In this case, the asymptote is \( y = 5 \). **Correct Option:** - **domain**: \( \{x \mid x \) is a real number \( \} \); - **range**: \( \{y \mid y > 5\} \); - **asymptote**: \( y = 5 \). **Answer:** Exactly the first option:  domain: all real numbers;  range: all real y with y > 5;  asymptote: y = 5.