a function has an initial value of -1 and a slope equal to 3 choose the sketch of a graph that exhibits the qualitative features of the function
To sketch a graph that exhibits the qualitative features of a function with an initial value of -1 and a slope of 3, we can use a linear function in the form of y = mx + b, where m represents the slope and b represents the initial value.
In this case, the equation of the function would be y = 3x - 1.
To plot the graph, we can start by identifying the y-intercept, which is the initial value of -1. This means that the graph will intersect the y-axis at the point (0, -1).
Next, we can use the slope of 3 to determine the next point on the graph. Since the slope is positive, the graph will have an upward direction. For every increase of 1 in the x-coordinate, the y-coordinate will increase by 3.
Using this information, we can plot a few more points. When x = 1, y = 3(1) - 1 = 3 - 1 = 2, giving us the point (1, 2). Similarly, when x = -1, y = 3(-1) - 1 = -3 - 1 = -4, giving us the point (-1, -4).
Now, connect these points with a straight line, since the function is linear. The resulting graph would look like this:
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In this graph, the line starts at the y-intercept of -1, then slopes upwards with a slope of 3. The slope represents the rate of change of the function, indicating that for every 1 increase in the x-coordinate, the y-coordinate increases by 3.