Algebra 1 Georgia Milestones Review

Unit 5: Comparing and Contrasting Functions A family invested $2,000 into an account that pays 2% interest compounded annually. In the functions below, x represents time in years and y represents the total amount in the account after x years.

Distinguish between situations that can be F.LE.1 modeled with linear Use the function that models the situation correctly. To the nearest dollar, how much money is in the family account after 5 years? functions and with exponential functions. A) $2.081 B) $2,200 C) $2, 208 D) $10,200

Show that linear The following tables show the values of different functions at various values of x. Identify each function as linear, exponential, or functions grow by equal neither. differences over equal intervals and that exponential functions grow by equal factors over equal intervals. (This F.LE.1a can be shown by algebraic proof, with a table showing differences, or by calculating average rates of change over equal intervals). The table represents the world population (in billions) and the year it was reached. Based on the data in the table below, would a linear function be an appropriate model? Explain why or why not.

Recognize situations in 1804 1 which one quantity 1927 2 F.LE.1 changes at a constant 1960 3 b rate per unit interval 1974 4 relative to another. 1987 5 1999 6 2012 7

F.LE.1c Recognize situations in For each or the scenarios below, decide whether or not the situation can be modeled by an exponential function. which a quantity grows or decays by a constant percent rate per unit interval relative to another. a. From 1910 until 2010 the growth rate of the United States has been steady at about 1.5% per year. The population in 1910 was

about 92,000,000.

1. b. The circumference of a circle as a function of the radius.

2. c. According to an old legend, an Indian King played a game of chess with a traveling sage on a beautiful, hand-made

chessboard. The sage requested, as reward for winning the game, one grain of rice for the first square, two grains for the second,

four grains for the third, and so on for the whole chess board. How many grains of rice would the sage win for the nth square?

4. d. The volume of a cube as a function of its side length. Algebra 1 Georgia Milestones Review

A certain car depreciates at a rate of 15% per year. If the purchase price of the car is $26,000, what will be the value of the car after 6 years?

A) $3,900 B) $9,806 Construct linear and C) $22,100 exponential functions, D) $22,609 including arithmetic and geometric sequences, Which rule applies to the table below? given a graph, a F.LE.2 description of a relationship, or two input-output pairs (include reading these A) from a table). B)

The first four terms of two different sequences are shown below. Sequence 𝐴 is

given in the table, and sequence 𝐵 is graphed as a set of ordered pairs.

Observe using graphs and tables that a quantity increasing exponentially eventually exceeds a F.LE.3 quantity increasing linearly, quadratically, or (more generally) as a polynomial function.

Which sequence will be the first to exceed 500? How do you know? Interpret the parameters The number of bacteria present in a laboratory sample after t days can be represented by . What is the initial number of bacteria in a linear (f(x) = mx + b) present in this sample? and exponential ( f(x) = a dx ) function in terms of A) 250 context. (In the functions B) 500 above, “m” and “b” are C) 750 the parameters of the D) 1000 linear function, and “a” F.LE.5 and “d” are the The function y = 6 + 1.25x can be used to find the cost of joining an online music club and buying x songs from the website. Based parameters of the on this information, which statement about the graph of this situation is true? exponential function.) In context, A) The y-intercept of the graph represents the cost of each song. students should describe B) The y-intercept of the graph represents the cost of joining the music club. what these parameters C) The slope of the graph represents the total number of songs bought by members of the club. mean in terms of change D) The slope of the graph represents the number of songs each member buys when visiting the website. and starting value. F.BF.3 Identify the effect on the The graph of is translated up 5 units. What is the equation of the new graph? graph of replacing f(x) by f(x) + k, k f(x), f(kx), and A) f(x + k) for specific values of k(both positive and B) negative); find the value of k given the graphs. C) Algebra 1 Georgia Milestones Review

D) Experiment with cases and illustrate an If c = −5, how does the graph of compare to the graph of ? explanation of the effects on the graph using A) The graph of is below the graph of . technology. Include recognizing even and odd B) The graph of is above the graph of . functions from their graphs and algebraic C) The graph of is narrower than the graph of . expressions for them. D) The graph of is wider than the graph of .

Which of the following mappings best represents the function f(x) = −x2 + 3? Understand that a function from one set A) (the input, called the domain) to another set (the output, called the range) assigns to each element of the domain exactly one element of F.IF.1 the range, i.e. each input B) value maps to exactly one output value. If f is a function, x is the input (an element of the domain), and f(x) is the output (an element of the range). Graphically, C) the graph is y = f(x).

F.IF.2 Use function notation, Jamie has a plan to save money for a trip. Today, she put 5 pennies in a jar. Tomorrow, she will put the initial amount plus another evaluate functions for 5 pennies. Each day she will put 5 pennies more than she put into the jar the day before, as shown in the table. inputs in their domains, and interpret statements that use function notation in terms of a Let represent the amount of pennies she puts into the jar on day d. What does mean? context. A) Jamie will put 10 pennies in the jar on day 55.

B) Jamie will put 55 pennies in the jar on day 10.

C) Jamie will have 10 pennies in the jar on day 55.

D) Jamie will have 55 pennies in the jar on day 10. Algebra 1 Georgia Milestones Review

The table below shows ordered pairs of a linear function.

Using tables, graphs, and verbal descriptions, interpret the key characteristics of a function which models the relationship between two quantities. Sketch a graph showing key F.IF.4 features including: What are the x- and y-intercepts for the graph of this linear function? intercepts; interval where the function is A) x-intercept: (−6, 0) increasing, decreasing, y-intercept: (0, 9) positive, or negative; relative maximums and B) x-intercept: (0, −6) minimums; symmetries; y-intercept: (9, 0) end behavior C) x-intercept: (0, 9) y-intercept: (−6, 0)

D) x-intercept: (9, 0) y-intercept: (0, −6) 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 F.IF.5 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. Given the functions g(x), f(x), and h(x) shown below:

Calculate and interpret the average rate of change of a function (presented symbolically F.IF.6 or as a table) over a specified interval. Estimate the rate of change from a graph. The correct list of functions ordered from greatest to least by average rate of change over the interval is

A) f(x), g(x), h(x) B) h(x), g(x), f(x) C) g(x), f(x), h(x) D) h(x), f(x), g(x) Graph functions On the coordinate plane provided, graph the line with equation . Identify the x- and y-intercepts. F.IF.7 expressed algebraically Algebra 1 Georgia Milestones Review

and show key features of the graph both by hand and by using technology.

A portion of the graph of a quadratic function f(x) is shown in the xy-plane. Selected values of a linear function g(x) are shown in the table.

Use a comparison symbol ( =, >, <, >, < ) to indicate the relationship between the first and second quantity.

Compare properties of two functions each represented in a different way (algebraically, graphically, numerically F.IF.9 in tables, or by verbal descriptions). For example, given a graph of Compare the following three functions. one function and an algebraic expression for another, say which has i. A function 𝑓 is represented by the graph below the larger maximum.

ii. A function 𝑔 is represented by the following equation.

𝑔(𝑥) = (𝑥 − 6)2 – 36 Algebra 1 Georgia Milestones Review

iii. A linear function ℎ is represented by the following table

For each of the following, evaluate the three expressions given, and identify which expression has the largest value and which has the smallest value. Show your work.

a. 𝑓(0), 𝑔(0), ℎ(0)

b. 𝑓(1000), 𝑔(1000), ℎ(1000)