FREE NJGPA Interpreting Functions and Key Features from Graphs and Tables (Algebra I) Questions and Answers

Question 1

A function is represented by a continuous graph that starts at the point (-4, 2) and ends at the point (5, -1). What is the domain of the function?

Accepted Answer

[-4, 5]

Answer

The domain of a function refers to all possible x-values. Since the graph is continuous and extends from an x-value of -4 to an x-value of 5, inclusive, the domain is all real numbers between -4 and 5, which is written as [-4, 5] or -4 ≤ x ≤ 5.

Question 2

Consider the function f(x) represented by the table of values below. What is the y-intercept of the function?  Table: x: -2, -1, 0, 1, 2; f(x): 9, 6, 3, 0, -3

Accepted Answer

(0, 3)

Answer

The y-intercept is the point where the graph of the function crosses the y-axis. This always occurs when the x-value is 0. According to the table, when x = 0, the value of f(x) is 3, so the y-intercept is (0, 3).

Question 3

The graph of a parabola opens downwards and has its vertex at the point (2, 8). On which interval is the function increasing?

Accepted Answer

(-∞, 2)

Answer

Since the parabola opens downwards, the function's values increase as x approaches the vertex from the left and decrease as x moves away from the vertex to the right. The x-coordinate of the vertex is 2. Therefore, the function is increasing on the interval from negative infinity up to 2, which is written as (-∞, 2).

Question 4

The graph shows the height of a ball thrown into the air over time. The highest point on the graph is (3, 25). What is the maximum height the ball reaches?

Accepted Answer

25

Answer

The maximum value of a function shown on a graph corresponds to the y-coordinate of the highest point (the vertex or a peak). In this case, the point (3, 25) means that at 3 seconds (x-value), the height is 25 feet (y-value). Therefore, the maximum height is 25.

Question 5

A function is defined by the following table of values. What is the average rate of change over the interval from x = 1 to x = 4? Table: x: 0, 1, 2, 3, 4; f(x): 2, 5, 10, 17, 26

Accepted Answer

7

Answer

The average rate of change is calculated as the change in y divided by the change in x, or (f(b) - f(a)) / (b - a). Here, a=1 and b=4. From the table, f(4) = 26 and f(1) = 5. So, the calculation is (26 - 5) / (4 - 1) = 21 / 3 = 7.

(NJGPA) New Jersey Graduation Proficiency Assessment Practice Test

(NJGPA) New Jersey Graduation Proficiency Assessment Practice Test

FREE NJGPA Interpreting Functions and Key Features from Graphs and Tables (Algebra I) Questions and Answers