NJGPA Interpreting Functions and Key Features from Graphs and Tables (Algebra I) 3 — Questions and Answers
Question 1: A graph of h(x) has zeros at x = -3, x = 1, and x = 5. How many times does the graph cross the x-axis?
- 1
- 2
- 3 (Correct answer)
- 5
Correct answer: 3
Each zero corresponds to one x-intercept, so the graph crosses the x-axis 3 times.
Question 2: A function's table shows inputs 1–5 and the same output value of 7 for each. What is true?
- The function is linear with slope 7
- The function is constant (Correct answer)
- The function is undefined
- The function has no y-intercept
Correct answer: The function is constant
When all outputs are equal regardless of input, the function is constant.
Question 3: On a graph, f(x) increases steeply from x = 0 to x = 2, then levels off. What does the 'leveling off' indicate?
- The function becomes undefined
- The rate of change is decreasing toward zero (Correct answer)
- The function has a zero at x = 2
- The function becomes negative
Correct answer: The rate of change is decreasing toward zero
Leveling off means the function's rate of change is slowing and approaching zero.
Question 4: A linear function has a negative slope. Which table correctly represents this?
- x: 1,2,3 y: 2,4,6
- x: 1,2,3 y: 10,7,4 (Correct answer)
- x: 1,2,3 y: 5,5,5
- x: 1,2,3 y: 1,4,9
Correct answer: x: 1,2,3 y: 10,7,4
A negative slope means y decreases as x increases; 10, 7, 4 decreases by 3 each step.
Question 5: The graph of g(x) is entirely below the x-axis. What can you conclude?
- g(x) > 0 for all x
- g(x) < 0 for all x (Correct answer)
- g(x) = 0 for all x
- g(x) has no y-intercept
Correct answer: g(x) < 0 for all x
A graph entirely below the x-axis means all output values are negative, so g(x) < 0.
Question 6: A function's graph touches the x-axis at x = 4 but does not cross it. What is true about x = 4?
- It is a zero of the function with even multiplicity (Correct answer)
- It is not a zero of the function
- It is a y-intercept
- It is a maximum of the function
Correct answer: It is a zero of the function with even multiplicity
When a graph touches but does not cross the x-axis, the zero has even multiplicity (like a double root).
Question 7: A table shows f(0)=3, f(2)=3, f(4)=3, f(6)=3. What is the slope of this function?
- 3
- 1
- 0 (Correct answer)
- Undefined
Correct answer: 0
When the output never changes, the slope is 0, representing a horizontal line.
NJGPA Interpreting Functions and Key Features from Graphs and Tables (Algebra I) 3
A graph of h(x) has zeros at x = -3, x = 1, and x = 5.
How many times does the graph cross the x-axis?