NJGPA Interpreting Functions and Key Features from Graphs and Tables (Algebra I) 2 — Questions and Answers
Question 1: A table shows x-values 0, 1, 2, 3 and y-values 5, 8, 11, 14. What is the rate of change?
- 2
- 3 (Correct answer)
- 5
- 8
Correct answer: 3
The y-value increases by 3 for each increase of 1 in x, so the rate of change is 3.
Question 2: On a graph of f(x), the function is above the x-axis for x < -2 and x > 4. Where is f(x) positive?
- -2 < x < 4
- x < -2 and x > 4 (Correct answer)
- x = -2 and x = 4
- x > 0
Correct answer: x < -2 and x > 4
A function is positive where its graph lies above the x-axis, which is x < -2 and x > 4.
Question 3: A function's graph shows a maximum value of 9 at x = 3. What does this vertex represent?
- The x-intercept of the function
- The highest output value the function reaches (Correct answer)
- The starting value of the function
- The point where the function crosses the y-axis
Correct answer: The highest output value the function reaches
The maximum value of 9 represents the highest output (y-value) the function achieves.
Question 4: A table for a linear function shows the points (2, 7) and (6, 15). What is the y-intercept?
- 1
- 2
- 3 (Correct answer)
- 7
Correct answer: 3
The slope is (15-7)/(6-2) = 2, so using point (2,7): 7 = 2(2) + b gives b = 3.
Question 5: A graph shows a function that is decreasing on the interval (1, 5). Which statement is true?
- f(1) < f(5)
- f(1) > f(5) (Correct answer)
- f(1) = f(5)
- f(3) is the minimum
Correct answer: f(1) > f(5)
A decreasing function has larger outputs at smaller inputs, so f(1) > f(5).
Question 6: The graph of a function passes through (0, -4). What does this point represent?
- An x-intercept
- The y-intercept (Correct answer)
- A zero of the function
- A maximum
Correct answer: The y-intercept
The point (0, -4) lies on the y-axis, making it the y-intercept of the function.
Question 7: A table shows a function with values: f(1)=2, f(2)=4, f(3)=8, f(4)=16. What best describes this function?
- Linear with slope 2
- Linear with slope 4
- Exponential (Correct answer)
- Quadratic
Correct answer: Exponential
Each output doubles the previous (multiplied by 2), which is the pattern of an exponential function.
NJGPA Interpreting Functions and Key Features from Graphs and Tables (Algebra I) 2
A table shows x-values 0, 1, 2, 3 and y-values 5, 8, 11, 14.
What is the rate of change?