Name: _____________ Class: ______ Algebra Quarterly 2 – Review Sheet 3

*Note: The supplementary questions are related to, but will not be on, Quarterly 2. But keep in mind that every supplementary question (as well as every question in Quarterly 2) comes directly from, or is similar

to, an actual Regents question.

Question 1 The function 𝑓(𝑥), which is graphed below, and the function 𝑔(𝑥) = −|𝑥| − 0.5 are given.

State whether each statement is true or false and explain. I. 𝑔(𝑥) has a lower minimum than 𝑓(𝑥) II. 𝑓(𝑥) has a lower maximum than 𝑔(𝑥) III. For all values of x, 𝑔(𝑥) < 𝑓(𝑥) IV. For every value of x, 𝑓(𝑥) ≠ 𝑔(𝑥) V. 𝑔(𝑥) and 𝑓(𝑥) have the same domain. VI. 𝑔(𝑥) and 𝑓(𝑥) have the same range.

Supplementary Question:

Question 2

Supplementary Question:

Supplementary Question: Solve each system of equations below

Question 3

Supplementary Question:

Question 4

Supplementary Question: A population of rabbits in a lab, 𝑝(𝑥), can be modeled by the function 𝑝(𝑥) = 20(1.014)2, where x represents the number of days since the population was first counted. Determine, to the nearest tenth, the average rate of change from day 50 to day 100.

Question 5 Graph 𝑎(𝑥) = √𝑥 − 2 + 3 and 𝑏(𝑥) = 8

9𝑥 + 2 on the grid below. State all solutions to 𝑎(𝑥) = 𝑏(𝑥) and

explain how you know using the graph.

Supplementary Question: Graph 𝑎(𝑥) = 8

2 and 𝑏(𝑥) = 𝑥 on the grid below. State all solutions to 𝑎(𝑥) = 𝑏(𝑥) and explain how you know

using the graph.

Question 6 Identify the domain and range of each function below:

Supplementary Question: For function graphed below, over which of the following intervals is decreasing? (1)

(2)

(3)

(4)

Supplementary Question: A function is initially defined by the set of coordinate pairs . Which coordinate pair below,

if added to this set, prevents the set from representing a function? (1) (3) (2) (4)

( )g x ( )g x

1 5x< <

1 3x- < <

6 4x- < <

3 1x- < <

( ) ( ) ( ){ }3, 7 , 1, 5 , 4,13-

( )2, 5 ( )1, 8-

( )5, 0 ( )1, 4-

Question 7 The graph below represents national and New York State average gas prices.

If New York State’s gas prices are modeled by 𝐺(𝑥) and 𝐶 > 0, which expression best approximates the national average x months from August 2014? 1) 𝐺(𝑥 + 𝐶) 2) 𝐺(𝑥) + 𝐶 3) 𝐺(𝑥 − 𝐶) 4) 𝐺(𝑥) − 𝐶 Supplementary Question: How many zeros does the graph below have? Identify them by circling or drawing arrows. Do not identify their coordinates.

Supplementary Question: The function 𝑓(𝑥) is graphed on the set of axes below. On the same set of axes, graph 𝑓(𝑥 + 1) + 2.

Question 8 Jane is buying a fruit salad and potato salad for a picnic. Fruit salad costs $2.00 per pound and potato salad costs $4.00 per pound. Jane needs to buy at least 6 pounds of salads and she doesn’t want to spend more than $20. If x represents the pounds of fruit salad and y represents the pounds of potato salad, write and graph a system of linear inequalities to represent this situation and list 2 possible combinations of salad that Jane could buy.

Supplementary Question: Write the system of inequalities whose solution set is shown below: