1. **Problem statement:** Given four functions A, B, C, and D with their graphs described, answer the following: a) Which function is increasing and has the range $y \in \mathbb{R}$ and $y \geq 0$? b) Find the value of function D at $x=0$. 2. **Step a) Identify the function:** - Function A is an increasing exponential curve passing through $(0,1)$ and approximately $(1,2)$. - Function B is a steep increasing line passing through $(0,-2)$, $(1,0)$, and $(2,2)$. - Function C is an increasing square root curve starting at $(0,0)$, passing through $(1,1)$ and approximately $(2,1.4)$. - Function D is a downward opening parabola with vertex at $(1,0)$, passing through $(0,-1)$ and $(2,-1)$. The function must be increasing and have range $y \geq 0$. - Function A (exponential) is increasing and its range is $y > 0$ (which is $y \geq 0$ if we consider the limit). - Function C (square root) is increasing and its range is $y \geq 0$. Since the problem states $y \in \mathbb{R}$ and $y \geq 0$, meaning all real numbers greater or equal to zero, function C fits perfectly. **Answer:** Function C. 3. **Step b) Find $D(0)$:** Function D is a downward opening parabola with vertex at $(1,0)$ and passes through $(0,-1)$. Therefore, the value of function D at $x=0$ is $-1$. **Answer:** $D(0) = -1$.