The graph of y= 2a +5 looks like: -10 10 1,0 We should notice that our line's y-values may change from positive to negative (or vice versa) only where the graph crosses the x-axis (the x-intercept, which can also be called a "root"). 1,0 If we're looking at where our line has positive or negative y-values (range), we need to look at our set of inputs (domain). If we view the domain as separate intervals, split at the x-intercept, we know that the line must be either positive or negative for the entire interval (since our function may only "change signs" at the x-intercept). -9 -8 Because our function must be either positive or negative for each interval, we only need to "test" our y -coordinates for one a-value in each interval. (-inf,) Identify roots and asymptotes Test each interval -7 -6 -5 -4 a. Select an x-value in the first interval, (-∞, - $): -2 -18 12 Evaluate the function f(x) at your selected. x-value: Will f(x) be positive or negative on the first interval? Negative v b. Select an x-value in the second interval, (-1,00): 0 And evaluate the function f(x) at your selected x-value: 5 16 (,inf) 3 4 5 6 7 8 9 (