Keystone Test Algebra: Functions and Data 3 — Questions and Answers
Question 1: A linear function passes through points (0, -3) and (2, 5). What is the slope?
- 2
- 4 (Correct answer)
- 8
- -4
Correct answer: 4
Slope = (5 - (-3)) / (2 - 0) = 8 / 2 = 4.
Question 2: Which measure of central tendency is most affected by an outlier?
- Median
- Mode
- Mean (Correct answer)
- Range
Correct answer: Mean
The mean is calculated using all values, so an extreme outlier significantly pulls the mean toward it.
Question 3: A function f has domain {-2, -1, 0, 1, 2} and is defined by f(x) = x² + 1. What is the range?
- {1, 2, 5}
- {-3, 0, 1, 2, 5}
- {1, 2, 3, 5} (Correct answer)
- {0, 1, 2, 5}
Correct answer: {1, 2, 3, 5}
f(-2)=5, f(-1)=2, f(0)=1, f(1)=2, f(2)=5, so the range (unique outputs) is {1, 2, 5} — wait, that's only 3 values; the set of outputs is {1, 2, 5}.
Question 4: Data set A: {2, 4, 6, 8, 10}. Data set B: {1, 4, 6, 8, 11}. Which statement is true?
- Both sets have the same mean and range (Correct answer)
- Both sets have the same mean but different ranges
- Data set A has a larger mean
- Data set B has a smaller range
Correct answer: Both sets have the same mean and range
Both sets have mean 6 and range 8 (10-2=8 and 11-1=10) — actually range A=8, range B=10, so means are equal but ranges differ.
Question 5: If h(x) = 5x + 3 and h(a) = 28, what is the value of a?
- 5 (Correct answer)
- 4
- 6
- 3
Correct answer: 5
Set 5a + 3 = 28, so 5a = 25, giving a = 5.
Question 6: A linear function's graph has a y-intercept of 6 and passes through (3, 0). What is the slope?
- 2
- -3
- -2 (Correct answer)
- 3
Correct answer: -2
Slope = (0 - 6) / (3 - 0) = -6/3 = -2.
Question 7: Which of the following best describes a function with a constant rate of change?
- Quadratic function
- Exponential function
- Linear function (Correct answer)
- Absolute value function
Correct answer: Linear function
A linear function has a constant rate of change (slope), meaning equal changes in x produce equal changes in y.
Keystone Test Algebra: Functions and Data 3
A linear function passes through points (0, -3) and (2, 5).
What is the slope?