equation of the new function, $g(x)$ ? \[ g(x)=10-1.0 \cdot 0.5^{x} \] State the $y$-intercept of $g(x)$. \[ (x, y)=\left(0,9 \quad x_{x}\right) \] State the domain and range of $g(x)$. (Enter your answers using interval notation.) \[ \text { domain }-\infty, \infty \] range \[ \infty, \infty \]

Step 1 ：The function given is \(g(x)=10-1.0 \cdot 0.5^{x}\).

Step 2 ：The y-intercept of a function is the point where the function crosses the y-axis. This occurs when x = 0.

Step 3 ：Substituting x = 0 in the function, we get the y-intercept as \((0, 9)\).

Step 4 ：The domain of a function is the set of all possible x-values. Since there are no restrictions on x in the given function, the domain is all real numbers, which in interval notation is \((-\infty, \infty)\).

Step 5 ：The range of a function is the set of all possible y-values. Since the function is decreasing and approaches 10 as x approaches infinity, the range is \((-\infty, 10]\).

Step 6 ：\(\boxed{\text{The y-intercept of the function } g(x)=10-1.0 \cdot 0.5^{x} \text{ is } (0, 9). \text{ The domain of the function is } (-\infty, \infty) \text{ and the range of the function is } (-\infty, 10]}\)