Function Check
The relation is {(−3, 2), (0, 5), (4, 2), (7, 9)}. Is it a function?
The relation is {(−3, 2), (0, 5), (4, 2), (7, 9)}. Is it a function?
The y-values are 4, 9, 14, 19 as x increases by 1. Name the family.
Linear. The first difference is constantly +5.
For y = 5x − 2 with no stated restrictions, give the domain and range
Domain: all real numbers. Range: all real numbers.
Find the next term in 11, 17, 23, 29, …
35. The common difference is 6.
For y = −4x + 9, identify the slope and y-intercept
Slope −4. The y-intercept is (0, 9)
A table pairs x-values 1, 2, 3, 4 with y-values 6, 6, 8, 10. Does the table define y as a function of x?
Yes. Repeated outputs are allowed. Each x-value has one y-value.
The y-values are 3, 12, 48, 192 as x increases by 1. Name the family.
Exponential. Each output is multiplied by 4.
A theater sells at most 250 tickets. Let n be the number sold. Give a reasonable domain for n.
Whole numbers from 0 through 250.
Find the 9th term of 5, 8, 11, 14, …
29. Use a₉ = 5 + 8(3)
Write the equation of the line with slope 3 through (0, −5)
y = 3x − 5
The relation is {(2, −1), (5, 3), (2, 7), (8, 4)}. Explain why it fails the function test.
Input 2 has two outputs, −1 and 7, so the relation is not a function.
The y-values are 7, 4, 3, 4, 7 for equally spaced x-values. Name the family and state the evidence.
Quadratic. The first differences are −3, −1, 1, 3, so the second differences are constantly 2.
Give the domain and range of y = (x + 1)² − 9.
Domain: all real numbers. Range: y ≥ −9.
Write an explicit rule for 80, 40, 20, 10, …
aₙ = 80(1/2)(n − 1)
Find the equation of the line through (2, 7) and (6, 15)
The slope is 2, so y = 2x + 3
Each book in a library is paired with its author. Must this relation always be a function from books to authors?
No. A book can have more than one author, so one input may have multiple outputs.
Which family fits the table x: 0, 1, 2, 3 and y: −2, 1, 10, 25?
Quadratic. First differences are 3, 9, 15 and second differences are constantly 6.
A candle is 18 cm tall and burns 1.5 cm per hour. Give the reasonable domain and range for h(t) = 18 − 1.5t.
Domain: 0 ≤ t ≤ 12. Range: 0 ≤ h ≤ 18. Both are continuous.
An arithmetic sequence has a₁ = −7 and d = 4. Find a₁₅ and write the explicit rule.
aₙ = −7 + 4(n − 1), and a₁₅ = 49
A line of best fit for temperature x and drink sales y is y = 6.2x − 210. Predict sales when x = 50
100 drinks, because 6.2(50) − 210 = 100
A graph contains a filled point at (3, 1), an open point at (3, 6), and no other point with x = 3. Does x = 3 violate the vertical line test?
No. The open point is not included, so x = 3 has only the output 1.
A function has a constant percent increase for equal changes in x. Which family fits, and what table pattern should appear?
Exponential. Consecutive outputs have a constant ratio.
Give the domain and range of y = 7(0.6)^x
Domain: all real numbers. Range: y > 0
A geometric sequence has a₃ = 45 and positive ratio r = 3. Find a₁ and write the explicit rule.
a₁ = 5. The rule is aₙ = 5(3)(n − 1)
Data points are (1, 12), (2, 15), (3, 19), (4, 22), (5, 27). Give a reasonable line of best fit and predict y at x = 6
One reasonable regression model is y ≈ 3.7x + 7.9, which predicts y ≈ 30.1 at x = 6