What you’ll learn
Identify intercepts, intervals, maxima/minima.
Key idea
Track how outputs change from left to right on both sides of the turning point.
Extremum compares output heights; leftmost input is not automatically the lowest or highest output.
Worked example
Classify examples and non-examples for the concept 'Identify intercepts, intervals, maxima/minima'.
Continuous graph is exactly the straight segments joining (-7,4),(-3,-4),(1,4), domain [-7,1]. Classify the statement "minimum output is -4 at x=-3" with evidence.
Marked coordinates: E=(-7, 4); E=(1, 4); V=(-3, -4).
- The complete graph consists of straight segments from (-7,4) through (-3,-4) to (1,4).
- It decreases on [-7,-3] and increases on [-3,1]; the minimum output is -4 at x=-3. Extremum compares output heights, not input order.
Answer: True — the turning point is the lowest output on both complete segments.
Quick Check
Classify examples and non-examples for the concept 'Identify intercepts, intervals, maxima/minima'.
Continuous graph is exactly the straight segments joining (-5,-8),(-3,-2),(-1,-8), domain [-5,-1]. Classify the statement "maximum output is -2 at x=-3" with evidence.
Marked coordinates: V=(-3, -2); E=(-5, -8); E=(-1, -8).