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M1-027-A09-V04
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F-IF.9
Warmup
M1-027-A09-V04
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 \(L(x)~=~-2x~+~3\) and \(Q(x)~=~-(x~-~1)^{2}~+~5\) on all real inputs. State each function's rate behavior, extrema, interval behavior, and their key contrast.
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A
L = decreasing line with constant slope -2 and no global extremum; Q = upward quadratic with changing rate and minimum (1,5), decreasing then increasing; contrast = L has constant decrease while Q has a minimum
B
L = decreasing line with constant slope -2 and maximum (1,5); Q = downward quadratic with changing rate and no extremum, decreasing for all x; contrast = both have no turning point
C
L = decreasing line with constant slope -2 and no global extremum; Q = downward quadratic with constant slope -2 and no extremum, decreasing for all x; contrast = both decrease at one constant rate
D
L = decreasing line with constant slope -2 and no global extremum; Q = downward quadratic with changing rate and maximum (1,5), increasing on (-∞,1] then decreasing on [1,∞); contrast = L decreases at one rate while Q turns at x=1
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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
