which key features were used to sketch this graph?\nthe function is continuous. the y - intercept is 0. the…

which key features were used to sketch this graph?\nthe function is continuous. the y - intercept is 0. the real zeros are between - 2 and - 1, and at 0. the relative maximum is at (1,4.5). the relative minimum is at (2.25, 1.75). as x→ - ∞, f(x)→+∞ and as x→+∞, f(x)→+∞.\nthe function is continuous. the y - intercept is 0. the real zero is between - 2 and - 1. the relative maximum is at (2.25, 1.75). the relative minimum is at (1,4.5). as x→ - ∞, f(x)→ - ∞ and as x→+∞, f(x)→+∞.\nthe function is continuous. the y - intercept is 0. the real zeros are between - 2 and - 1, and at 0. the relative maximum is at (2.25, 1.75). the relative minimum is at (1,4.5). as x→ - ∞, f(x)→+∞ and as x→+∞, f(x)→+∞.\nthe function is continuous. the y - intercept is 0. the real zero is between - 2 and - 1. the relative maximum is at (1,4.5). the relative minimum is at (2.25, 1.75). as x→ - ∞, f(x)→ - ∞ and as x→+∞, f(x)→+∞.
Answer
Explanation:
Step1: Analyze the continuity
Since the graph is a smooth curve without breaks, the function is continuous.
Step2: Check the y - intercept
The graph passes through the origin ((0,0)), so the (y) - intercept is (0).
Step3: Locate the real zeros
The graph crosses the (x) - axis between (-2) and (-1) and at (x = 0).
Step4: Identify the relative extrema
The "highest" point (relative maximum) occurs at ((1,4.5)) and the "lowest" point (relative minimum) occurs at ((2.25,1.75)).
Step5: Determine the end - behavior
As (x\to-\infty) and (x\to+\infty), the graph goes up, so (f(x)\to+\infty) as (x\to-\infty) and (x\to+\infty).
Answer:
The function is continuous. The (y) - intercept is (0). The real zeros are between (-2) and (-1), and at (0). The relative maximum is at ((1,4.5)). The relative minimum is at ((2.25,1.75)). As (x\to-\infty,f(x)\to+\infty) and as (x\to+\infty,f(x)\to+\infty).