Question

1. consider the curve $y = 5(2^x)$. 13b can the function value ever be negative? the correct option was b yes no b 13c what is the domain of the function? $x \geq 2$ $x < 5$ $x \geq 0$ all real x

Explanation:

Step1: Analyze the function type

The function is \( y = 5(2^{x}) \), which is an exponential function. For any real number \( x \), the base of the exponential function \( 2^{x} \) has a specific range.

Step2: Determine the range of \( 2^{x} \)

For the exponential function \( a^{x} \) where \( a>1 \) (here \( a = 2>1 \)), the range of \( 2^{x} \) for all real \( x \) is \( (0,+\infty) \), that is, \( 2^{x}>0 \) for any real number \( x \).

Step3: Determine the domain of the function

Since there are no restrictions on the input \( x \) for the exponential function \( 2^{x} \) (we can plug in any real number \( x \) and get a valid output for \( 2^{x} \), and then multiply by 5), the domain of the function \( y = 5(2^{x}) \) is all real numbers.

Answer:

all real \( x \)