- Prove that linear functions grow by equal differences over equal intervals, and that exponential functions grow by equal factors over equal intervals.
- Recognize situations in which one quantity changes at a constant rate per unit interval relative to another.
- Recognize situations in which a quantity grows or decays by a constant percent rate per unit interval relative to another.
Clusters should not be sorted from Major to Supporting and then taught in that order. To do so would strip the coherence of the mathematical ideas and miss the opportunity to enhance the major work of the grade with the supporting clusters.
TEST ITEM SPECIFICATIONS
This benchmark may be assessed using:
- Assessment Limits :
Exponential functions should be in the form
- Calculator :
- Clarification :
Students will determine whether the real-world context may be
represented by a linear function or an exponential function and give
the constant rate or the rate of growth or decay.
Students will choose an explanation as to why a context may be
modeled by a linear function or an exponential function.
Students will interpret the rate of change and intercepts of a linear
function when given an equation that models a real-world context.
Students will interpret the x-intercept, y-intercept, and/or rate of
growth or decay of an exponential function given in a real-world
- Stimulus Attributes :
Items should be set in a real-world context.
Items must use function notation.
- Response Attributes :
Items may require the student to apply the basic modeling cycle.
Items may require the student to choose a parameter that is
described within the real-world context.
Items may require the student to choose an appropriate level of
Items may require the student to choose and interpret the scale in a
Items may require the student to choose and interpret units.
SAMPLE TEST ITEMS (1)
- Test Item #: Sample Item 1
The graph of function f models the specific humidity in the atmosphere, in grams of water vapor per kilogram of atmospheric gas , versus temperature, in degrees Celsius (ºC), as shown. Four of its points are labeled.
This question has two parts.
Felicia wants to model the raltionship between temperature, in ºC, and specific humidity, in . Select words to complete the statement about the type of model Felicia should use.
The relationship is _____________ because the specific humidity increases by equal ______ over equal intervals of temperature.
Which relationship must be true to justify the function type that models the relationship?
- Difficulty: N/A
- Type: : Multiple Types