Algebra: Functions and Data Flashcards

The line of best fit for a data set is y = 1.5x + 2. Predict y when x = 10.

Answer: 17

y = 1.5(10) + 2 = 15 + 2 = 17.

Which value is NOT in the range of f(x) = x² for all real numbers x?

Answer: -1

x² is always non-negative, so -1 cannot be an output of f(x) = x².

A box plot shows a minimum of 10, Q1 of 20, median of 30, Q3 of 45, and maximum of 60. What is the interquartile range (IQR)?

Answer: 25

IQR = Q3 - Q1 = 45 - 20 = 25.

Two functions: f(x) = 2x + 1 and g(x) = -x + 7. At what x-value do they intersect?

Answer: x = 2

Set 2x + 1 = -x + 7: 3x = 6, so x = 2.

If the graph of f(x) is shifted up 3 units, which new function results?

Answer: f(x) + 3

Adding a constant k outside the function, f(x) + k, shifts the graph up by k units.

A data set has values 5, 10, 10, 15, 20. Which of the following is true?

Answer: Mean = Median

Mean = (5+10+10+15+20)/5 = 60/5 = 12; Median = 10 — actually mean=12 > median=10, so Mean > Median.

Which situation can be modeled by a linear function?

Answer: Water draining from a tank at a constant rate of 5 gallons per minute

A constant rate of change (5 gallons per minute) produces a linear relationship between time and the amount of water.