Algebra: Functions and Data Flashcards

A function is defined as f(x) = 3x² - 2x + 1. What is f(-2)?

Answer: 17

f(-2) = 3(-2)² - 2(-2) + 1 = 3(4) + 4 + 1 = 12 + 4 + 1 = 17.

Which scatter plot description indicates a strong negative correlation?

Answer: Points cluster tightly along a line going down to the right

A strong negative correlation means as x increases, y decreases, shown by points tightly clustered along a downward-sloping line.

The table shows: x = {1, 2, 3, 4} and y = {5, 8, 11, 14}. Which function models this data?

Answer: y = 3x + 2

The common difference is 3 (slope), and when x=1, y=5: 3(1)+2=5, confirming y = 3x + 2.

If g(x) = 2x - 5, for what value of x does g(x) = 0?

Answer: x = 2.5

Set 2x - 5 = 0, so 2x = 5, giving x = 2.5.

A data set has values: 4, 7, 7, 9, 13. What is the mean of this data set?

Answer: 8

Mean = (4 + 7 + 7 + 9 + 13) ÷ 5 = 40 ÷ 5 = 8.

Which of the following represents a function?

Answer: {(1,2),(2,3),(3,4)}

A function requires each x-value to map to exactly one y-value; only {(1,2),(2,3),(3,4)} satisfies this.

The function f(x) = -x² + 4 has a maximum value. What is that maximum value?

Answer: 4

The parabola opens downward; its vertex is at (0, 4), so the maximum value is 4.