Building Functions

Which function best represents the graph?

• f(x) = x² – 7x – 8

• f(x) = x² – 4x + 2

• f(x) = x² – 2x – 8

• f(x) = x² + 2x – 8

Adriana deposits $480 into an account that earns 2.6% annual interest. She makes no further deposits or withdrawals. Which function models the total amount, j(t), in the account after t years?

• j(t) = t(480)^2.6

• j(t) = (480)^2.6t

• j(t) = 1.026(480)^t

• j(t) = 480(1.026)^t

Jacob and Heath install carpets. Jacob charges a flat fee of $112, plus $16 for each hour he works. Heath charges a flat fee of $200, plus $12 for each hour he works. Which function, p(x), represents the total amount of money, in dollars, they earn when they each work x hours?

• p(x) = 124x + 216

• p(x) = 124x + 88

• p(x) = 28x + 312

• p(x) = 28x + 88

The table shows the amount of mold, y, on a surface at various times, x.

Which function could be used to model the amount of mold on the surface after x minutes?

Which function models the data in the table?

The graph shows the number of bacteria in a petri dish over a period of time.

Which exponential function could be used to model the number of bacteria after x days?

Two cellphone companies have different charges for a cell phone plan. Caiden's provider charges $35 per month plus $0.03 per minute, x, for his phone plan. Jonas's provider charges $0.12 per minute, x, with no monthly fee for his phone plan. Which function represents the difference in cost between Caiden's and Jonas's plans?

• f(x) = ^–35x – 0.09

• f(x) = ^–35x + 0.09

• f(x) = ^–0.09x – 35

• f(x) = ^–0.09x + 35

At the end of December, Leo and Diego both earned a one-time bonus at work, plus their hourly wages. Leo's earnings are modeled by the function J(x) = 38.25x + 50.00. Diego’s earnings are modeled by the function E(x) = 30.20x + 52.00. Leo and Diego worked the same number of hours. If x represents hours worked, which function represents the total monthly earnings of Leo and Diego, M(x)?

• M(x) = 170.45x

• M(x) = 68.45x + 102.00

• M(x) = 88.25x + 82.20

• M(x) = 102.00x + 68.45

A shipping company started with 40 employees. The number of employees at the shipping company increases at a rate of 7.5% each year. Which function can be used to model the number of employees, f(x), at the shipping company after x years?

f(x) = 3x² + 7x and g(x) = 2x² - x - 1,
 find (f - g)(x).

• x² + 8x + 1

• x² + 6x - 1

• 5x² + 8x - 1

• x² + 8x -1