Linear Functions Flashcards

The function V(t) = 500 − 25t models the value (in dollars) of a laptop t months after purchase. After how many months will its value be $200?

Answer: 12

500 − 25t = 200 → 25t = 300 → t = 12.

What is the slope of a line that is parallel to the x-axis and passes through (2, −7)?

Answer: 0

A line parallel to the x-axis is horizontal and has slope 0.

Given f(x) = −2x + 10, over the interval 1 ≤ x ≤ 4, what is the difference f(1) − f(4)?

Answer: 6

f(1) = 8; f(4) = 2; f(1) − f(4) = 6.

A line has x-intercept 6 and y-intercept −4. What is the slope of the line?

Answer: 2/3

Using points (6, 0) and (0, −4): slope = (0 − (−4))/(6 − 0) = 4/6 = 2/3.

A taxi ride costs $3.00 plus $1.75 per mile. Which equation gives the total cost C for m miles and what is the cost for 8 miles?

Answer: C(m) = 1.75m + 3; $17.00

C(m) = 1.75m + 3; C(8) = 14 + 3 = $17.00.

For the linear function shown in the table, what is the equation? x: 0, 3, 6, 9 | y: −2, 4, 10, 16

Answer: y = 2x − 2

Rate of change = (4−(−2))/(3−0) = 2; y-intercept = −2 (when x = 0); y = 2x − 2.

If f(x) = 7x − 3 and g(x) = 7x + 5, which transformation maps the graph of f onto the graph of g?

Answer: Vertical shift up by 8 units

g(x) = f(x) + 8; adding 8 to the output shifts the graph up by 8 units.

The function A(d) = 2d + 50 represents the number of attendees at a weekly book club d weeks after it launched. How many more attendees will there be in week 10 than in week 4?

Answer: 12

A(10) = 70; A(4) = 58; 70 − 58 = 12. Alternatively: rate is 2 per week × 6 weeks = 12.