## Precalculus S1 V04

Domain:  Interpreting Functions (FIF)
 Learning Standard:  Interpret functions that arise in applications in terms of the context. Test Questions FIF09-12.04   For a function that models a relationship between two quantities, interpret key features of graphs and tables in terms of the quantities, and sketch graphs showing key features given a verbal description of the relationship. Key features include: intercepts; intervals where the function is increasing, decreasing, positive, or negative; relative maximums and minimums; symmetries; end behavior; and periodicity. 8, 9, 11, 26, 29 FIF09-12.05   Relate the domain of a function to its graph and, where applicable, to the quantitative relationship it describes. For example, if the function h(n) gives the number of person-hours it takes to assemble n engines in a factory, then the positive integers would be an appropriate domain for the function. 2, 3, 4, 5 Learning Standard:  Analyze functions using different representations. Test Questions FIF0912.07   Graph functions expressed symbolically and show key features of the graph, by hand in simple cases and using technology for more complicated cases. Graph rational functions, identifying zeros and asymptotes when suitable factorizations are available, and showing end behavior. 6, 7, 10, 12, 13, 21, 22, 23

Domain:  Building Functions (FBF)
 Learning Standard:  Build a function that models a relationship between two quantities. Test Questions FBF0912.01    Write a function that describes a relationship between two quantities.★ Compose functions. For example, if T(y) is the temperature in the atmosphere as a function of height, and h(t) is the height of a weather balloon as a function of time, then T(h(t)) is the temperature at the location of the weather balloon as a function of time. 16, 17, 18, 19 Learning Standard:  Build new functions from existing functions. Test Questions FBF09-12.03   Identify the effect on the graph of replacing f(x) by f(x) + k, k f(x), f(kx), and f(x + k) for specific values of k (both positive and negative); find the value of k given the graphs. Experiment with cases and illustrate an explanation of the effects on the graph using technology. Include recognizing even and odd functions from their graphs and algebraic expressions for them. 1, 14, 15, 49, 50 FBF0912.04   Find inverse functions. Verify by composition that one function is the inverse of another. Read values of an inverse function from a graph or a table, given that the function has an inverse. Produce an invertible function from a non-invertible function by restricting the domain. 20 FBF0912.05   Understand the inverse relationship between exponents and logarithms and use this relationship to solve problems involving logarithms and exponents. 33

Domain: Creating Equatiaons (ACED)
 Learning Standard:   Create equations that describe numbers or relationships. Test Questions ACED09-12.01   Create equations and inequalities in one variable and use them to solve problems. Include equations arising from linear and quadratic functions, and simple rational and exponential functions. 27, 28

Domain: Linear, Quadratic, and Exponential Models (FLE)
 Learning Standard:  Construct and compare linear, quadratic, and exponential models and solve problems. Test Questions FLE09-12.01   Distinguish between situations that can be modeled with linear functions and with exponential functions. 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. 24, 25 FLE09-12.04   For exponential models, express as a logarithm the solution to abct = d where a, c, and d are numbers and the base b is 2, 10, or e; evaluate the logarithm using technology. 30, 31

Domain: Trigonometric Functions (FTF)
 Learning Standard:  Extend the domain of trigonometric functions using the unit circle. Test Questions FTF09-12.01   Understand radian measure of an angle as the length of the arc on the unit circle subtended by the angle. 36, 37, 38, 39, 40 Learning Standard:  Model periodic phenomena with trigonometric functions. Test Questions FTF09-12.05   Choose trigonometric functions to model periodic phenomena with specified amplitude, frequency, and midline. 47, 48, 51 FTF0912.07   Use inverse functions to solve trigonometric equations that arise in modeling contexts; evaluate the solutions using technology, and interpret them in terms of the context. 52, 53, 54, 55 Learning Standard:  Prove and apply trigonometric identities. Test Questions FTF09-12.08    Prove the Pythagorean identity sin2(θ) + cos2(θ) = 1 and use it to find sin(θ), cos(θ), or tan(θ) given sin(θ), cos(θ), or tan(θ) and the quadrant of the angle. 35, 41, 42, 43, 44, 45, 46

Domain: Seeing Structure in Expressions (ASSE)
 Learning Standard:  Write expressions in equivalent forms to solve problems. Test Questions ASSE09-12.03   Choose and produce an equivalent form of an expression to reveal and explain properties of the quantity represented by the expression. Factor a quadratic expression to reveal the zeros of the function it defines. Complete the square in a quadratic expression to reveal the maximum or minimum value of the function it defines. Use the properties of exponents to transform expressions for exponential functions. For example the expression 1.15t can be rewritten as (1.151/12)12t ≈ 1.01212t to reveal the approximate equivalent monthly interest rate if the annual rate is 15%. 32, 34

TOTAL QUESTIONS = 55 questions