Unit 6 Live Classroom #2

The height of water in a bathtub, w, is a function of time, t. Let P represent this function, Height is measured in inches and time in minutes.

Match each description with the corresponding statement, written in function notation.

• P(4)=10

• The bathtub starts out with no water

• P(0)=0

• The height of the water is 10 inches after 4 minutes

• P(20)=0

• After 10 minutes, the height of the water is 4 inches

• P(10)=4

• After 20 minutes, the bathtub is empty

The function f gives the temperature, in degrees Celsius, t hours after midnight. Which function notation properly expresses the following statement?

"At 1:30pm, the temperature was 20 degrees Celsius."

• F(1.5)=20

• f(1:30)=20

• f(13.5)=20

• f(13:30)=20

Match each description to its corresponding function on the right.

• f(x)=2(x+4)

• To get the output, add 4 to the input then multiply the sum by 2

• h(x)=2x+4

• To get the output, multiply the input by 2 then add 4 to the product

• g(x)=4(x+2)

• To get the output, multiply the input by 4 then add 2 to the product

• k(x)=4x+2

• To get the output, add 2 to the input then multiply the sum by 4

The college student who is looking for a data plan for their cell phone found a third option, which also offers a 2-gigabyte monthly allowance for data. The monthly cost of this option can be represented by function C defined as C(x)=30x+5 where x is the gigabytes of data used over the monthly allowance.

C(0.7)=

The graph below represents Andre's distance from his bicycle as he walks in a park.

Which statements about the function and graph are true?

• The minimum of the graph is (17,1)

• A horizontal intercept of the graph represents the time when Andre was at his bike.

• The graph has multiple horizontal intercepts

• The graph has two maximums

• About 21 seconds after he left his bike, Andre was the farthest from it at about 8.3 feet.

A child tosses a baseball into the air. On its way down, the ball gets caught in a tree for several seconds before falling to the ground.

Sketch a graph that represents the height of the ball, h, as a function of time, t.

Be sure to label each axis.

The graph below represents two functions, f and g.

For each input value below, identify which function is greater.​

Groups:

(a) f(x) is greater than g(x)

,

(b) g(x) is greater than f(x)

,

(c) neither

• x=9

• x=10

• x=4

• x=8

• x=2

• x=6

The temperature was recorded at several times during the day. Function T gives the temperature in degrees Fahrenheit, n hours since midnight.

The graph of T is shown below.

For each time interval, identify the average rate of change as positive or negative.

Groups:

(a) positive average rate of change

,

(b) negative average rate of change

• from n=5 and n=7

• from n=10 to n=20

• from n=1 to n=5

• from n=20 to n=24

Diego's club earns money for charity when members of the club perform community service after school. For each student who does community service, the club earns $5. There are 12 students in the club.

The total dollar amount earned, E, is a function of the number of members who performs community service, n.

Which statement best describes the range of the function modeling the scenario?

• The range is all integers from 0 to 60

• The range is any multiple of 5 from 0 to 60

• The range is any positive value.

• The range is any value.

To raise funds for a trip, members of a high school math club are holding a game night in the gym. They sell tickets for $5 per person. The gym holds a maximum of 250 people. The amount of money raised is a function of the number of tickets sold.

Which equation best defines the function F as a function of the number of tickets sold, t, and the domain of the function?

• F(t)=5t, t≥250

• F(t)=250t, t≤5

• F(t)=250t, t≥5

• F(t)=5t, t≤250