Questions: Use the graph of the function t shown in the figure to the right to estimate the indicated function value. t(-3.1) ≈ (Type an integer or a decimal.)

Solution Steps

The x-value -3.1 lies between -4 and -3 on the x-axis.

The graph appears to be piecewise. The portion of the graph between x=-5 and x=0 is linear. At x = -4, the corresponding y-value is 1. At x=-3, the y-value is 2. Since -3.1 is closer to -3 than -4, we can estimate the y-value by observing that the graph passes through points that appear to be (-4,1), (-3,2), (-2,3), (-1,4) and (0,2). Since the line is relatively straight, the y-values at x = -3.1 will be approximately 2.

Since the graph is linear in this region, for each increase of 1 in x, there is an increase of 1 in y. Since -3.1 is slightly less than -3, the y-value should be slightly less than 2. The grid lines suggest the value is approximately 1.9.

Final Answer