Question

paring characteristics of functions
which function has a range limited to only negative numbers?
(images of four function graphs)
mark and return 9 of 10 save & exit

Explanation:

Step1: Analyze each graph's range

- First graph: The line goes from negative y (but also positive? Wait, no, let's check coordinates. Wait, the first graph: the vertex is at (2, -2)? Wait, no, the grid: y-axis, the first graph has points. Wait, maybe I misread. Wait, the fourth graph (bottom left): let's check. Wait, the question is which function has range limited to only negative numbers (y < 0 always).
- First graph: The line has a peak, but some points are above y=0? Wait, no, maybe the first graph's y-values: looking at the first graph, the line goes from lower left (negative y) up to a peak, then down. Wait, no, the y-axis: the first graph's grid, the y-axis has -2, -4, -6? Wait, maybe the first graph's y is negative? Wait, no, maybe I messed up. Wait, the fourth graph (bottom left): the line crosses the y-axis at -2, and goes down? Wait, no, let's check each:
1. Top left graph: The line has a vertex, and the y-values: the arrows go down, but does it have positive y? Wait, the grid: y-axis, the numbers are -2, -4, -6? Wait, maybe the first graph's y is negative? Wait, no, maybe the labels are reversed. Wait, the standard is y-axis up is positive. So top left: the line starts from bottom left (low y, maybe negative) up to a peak, then down. But does it ever go above y=0? Wait, the grid has y= -2, -4, -6? No, maybe the y-axis is labeled with positive up, so -2 is below origin, -4, -6. Wait, the first graph: the line goes from (let's say) x=-6, y=-10 (arrow) up to (2, -2) then down. So all y-values are negative? Wait, no, the peak is at y=-2? Wait, maybe the first graph's y is all negative. Wait, no, the second graph (top middle) is a parabola opening up, vertex at y=-4, so it goes from y=-4 up to positive. Third graph (top right): a curve starting at y=1 (positive) and decreasing, so y is positive or zero? Fourth graph (bottom left): a line with y-intercept at -2, slope negative, so y-values: when x increases, y decreases. Let's check the fourth graph: when x=-6, y=4? Wait, no, the bottom left graph: the line is from (-6, 4) down to (2, -2)? Wait, no, the grid: x from -6 to 6, y from -6 to 6. Wait, the bottom left graph: the line crosses the x-axis at ( -2, 0)? No, the bottom left graph: the line is going from top left (x=-6, y=4) down to (2, -2)? No, maybe I'm misinterpreting. Wait, the question is which function has range only negative numbers (y < 0 for all x in domain). Let's re-express:

- Top left graph: Let's see the y-values. The arrow at the bottom left is going down (more negative), and the peak is at y=-2 (since the grid has y=-2, -4, -6? Wait, no, the y-axis labels: the first graph has y=2, -2, -4, -6? Wait, no, the first graph's y-axis: the top is 2, then -2, -4, -6. So the line goes from (x=-6, y=-10) up to (x=2, y=-2) then down to (x=6, y=-10). So all y-values are ≤ -2, which are negative. Wait, but the fourth graph (bottom left): when x=-6, y=4 (positive), so that's positive. Top middle: parabola with vertex at y=-4, so it goes to positive y. Top right: starts at y=1 (positive). So the top left graph (first graph) has all y-values negative. Wait, but the user's image: let's check again. Wait, the first graph (top left) has a red line with arrows, the y-axis is labeled with 2, -2, -4, -6 (so 2 is above origin, -2 below). The line goes from the bottom left (arrow) up to a peak at (2, -2) then down. So all y-values are less than or equal to -2, which are negative. The fourth graph (bottom left) has a line that at x=-6, y=4 (positive), so that's positive. So the first graph (top left) has range limited to negative numbers. Wait, but maybe I made a mistake. Wait, the bottom left graph: the line is from (-6, 4) to (2, -2), so y goes from 4 (positive) to -2 (negative), so it has positive y-values. So the correct graph is the top left one? Wait, no, the first graph (top left) – let's check the y-axis: the numbers are 2, -2, -4, -6. So 2 is above origin, -2 is below. The line in the top left graph: the peak is at y=-2, and the arrows go down to more negative y. So all y-values are ≤ -2, which are negative. So the top left graph (first one) has range only negative numbers.

Step2: Confirm each graph's range

- Top left: All y-values are negative (≤ -2).
- Top middle: Parabola opens up, vertex at y=-4, so range is y ≥ -4 (includes positive).
- Top right: Curve starts at y=1 (positive) and decreases, so y ≥ 0 (or positive).
- Bottom left: Line with y-intercept -2, but when x=-6, y=4 (positive), so range includes positive.

So the top left graph (first one) has range limited to negative numbers.

Answer:

The graph on the Top Left