Question

state the domain and range using interval notation.
x ∈ ( select , select )
y ∈ ( select , select )

Explanation:

Step1: Analyze the domain

The graph is a curve (likely an exponential or logarithmic - type, but from the visual, it extends to the left infinitely and to the right infinitely? Wait, no, looking at the grid, the curve starts from the left (negative x - axis) and goes to the right (positive x - axis). Wait, actually, for the domain (x - values), the graph seems to cover all real numbers? Wait, no, maybe I missee. Wait, the graph is a curve that starts from the left (x approaching - infinity) and goes to the right (x approaching + infinity). Wait, but the interval notation for domain: if it's all real numbers, domain is $(-\infty, \infty)$. Wait, but let's check the graph again. The curve is a function that is defined for all real x? Wait, maybe it's an exponential function shifted? Wait, no, the key is to find the set of x - values (domain) and y - values (range) from the graph.

Looking at the graph, the curve extends to the left (x can be any real number, from negative infinity to positive infinity) because there's no break or restriction on the x - axis. So domain: $x\in(-\infty, \infty)$

Step2: Analyze the range

For the range (y - values), the lowest point of the curve: looking at the graph, the curve starts at y = - 4? Wait, no, the grid has a y - axis with - 5 at the bottom. Wait, the curve passes through (0, - 3)? Wait, no, maybe I should look at the minimum y - value. Wait, the curve is increasing, and as x approaches - infinity, what's the y - value? The curve seems to approach a horizontal asymptote at y = - 4? Wait, no, the graph shows that the curve starts from the left (x→-∞) with y approaching - 4 (or some constant) and then increases. Wait, actually, looking at the graph, the curve has a minimum y - value? Wait, no, the curve is increasing. Wait, when x = 0, y is - 3? Wait, no, maybe the range is from - 4 (or the horizontal asymptote) to infinity? Wait, no, maybe the range is $(-4, \infty)$? Wait, no, let's re - examine.

Wait, the graph: the curve is a function that is increasing, and as x→-∞, y approaches - 4 (the horizontal asymptote), and as x→+∞, y→+∞. So the range is $y\in(-4, \infty)$? Wait, no, maybe the horizontal asymptote is y = - 4, so the range is $(-4, \infty)$ because the function never actually reaches y = - 4 (since it's an asymptote) and goes to infinity as x increases.

Wait, but maybe I made a mistake. Let's start over.

Domain: The set of all x - values for which the function is defined. The graph shows that the function is defined for all real numbers (no gaps, no vertical asymptotes), so domain is $(-\infty, \infty)$

Range: The set of all y - values the function takes. The function starts from a horizontal asymptote (let's say y = - 4) and increases to infinity. So the range is $(-4, \infty)$

Wait, but maybe the horizontal asymptote is y = - 4, so the range is $(-4, \infty)$

Answer:

Domain: $x\in(-\infty, \infty)$; Range: $y\in(-4, \infty)$ (Note: The actual values may vary slightly depending on the exact graph, but the process is to identify the domain as all real numbers and the range as starting from the horizontal asymptote to infinity)