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M1-027-A09-V02
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F-IF.9
Warmup
M1-027-A09-V02
Compare two functions represented in different ways: equations, graphs, tables, or verbal descriptions.
Compare linear and quadratic graph features
Problem
Use the graphs and equations to compare \(L(x)~=~4\) and \(Q(x)~=~-(x~-~2)^{2}~+~9\). State their behavior, slope or extremum, ranges, intersections, and key contrast.
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A
L = constant function with slope 0 and range 4; Q = downward quadratic with maximum (2,9) and range (-∞,9]; intersections = x=2±5; contrast = L is constant while Q changes and has a maximum
B
L = increasing line with slope 4 and range all real numbers; Q = upward quadratic with minimum (2,9) and range [9,∞); intersections = x=2±√5; contrast = both increase away from their minimum
C
L = constant function with slope 0 and range 4; Q = downward quadratic with maximum (2,9) and range (-∞,9]; intersections = x=2±√5; contrast = L is constant while Q changes and has a maximum
D
L = constant function with slope 0 and range 4; Q = downward quadratic with maximum (2,9) and range (-∞,9]; intersections = none; contrast = a constant and quadratic cannot intersect
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Curriculum context
Standard F-IF.9
Category Functions
Domain Interpreting Functions
Objective Compare two functions represented in different ways: equations, graphs, tables, or verbal descriptions.
Problem type Compare linear and quadratic graph features
