Function Analysis and Water Depth Quiz

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Questions and Answers

Which statement correctly describes the independent variable in function F?

  • Time measured in minutes (correct)
  • Distance measured in kilometers
  • Walking speed in kilometers per minute
  • Duration of walking in hours

In the function $F(15) = 2$, the output represents the distance walked in kilometers.

True (A)

What does $h(125) = 400$ represent in the context of a plane's flight?

At 125 minutes after takeoff, the plane's height is 400 feet.

The vertical intercept in the graph of the football's flight represents where the football was ______.

<p>kicked</p> Signup and view all the answers

Match the following components of the football's flight graph with their meanings:

<p>Vertical intercept = Height where the football was kicked Horizontal intercept = Height when the football hit the ground Maximum height = The peak height reached by the football Minimum value = The lowest height of the football during its flight</p> Signup and view all the answers

What is the depth of the water in the pool after 6 minutes?

<p>5 inches (B)</p> Signup and view all the answers

The depth of water in the pool after 7 minutes is greater than after 10 minutes.

<p>False (B)</p> Signup and view all the answers

What value of m represents the distance at which both taxi companies charge the same amount?

<p>4.5</p> Signup and view all the answers

When the distance is 2 miles, the cost for Company B is approximately ______ dollars.

<p>7.425</p> Signup and view all the answers

Match the following depth of water in the pool with the corresponding time in minutes:

<p>0 minutes = 0 inches 5 minutes = X inches 7 minutes = 4 inches 10 minutes = Same depth as 15 minutes</p> Signup and view all the answers

What is the rate at which water drains from the pool?

<p>10 gallons per hour (D)</p> Signup and view all the answers

After 5 hours, there are 30 gallons of water remaining in the pool.

<p>False (B)</p> Signup and view all the answers

What is the equation used to determine the amount of water left in the pool after h hours?

<p>p(h) = 100 - 10h</p> Signup and view all the answers

The average rate of change in voter participation between 1996 and 2004 was approximately _____ million people per year.

<p>1.49</p> Signup and view all the answers

Match the following years with their corresponding number of voters (in millions) aged 18-29:

<p>1988 = 35.7 2008 = 48.4 2000 = 34.5 2016 = 43.4</p> Signup and view all the answers

Flashcards

Independent variable in function F

The independent variable in a function is the input value, in this case, time in minutes.

Dependent variable in function F

The dependent variable in a function F is the output value, in this case, distance in kilometers.

Function notation example F(15) = 2

F(15) = 2 means that when the input is 15 minutes, which is x the output, or F(x), is 2 kilometers.

Vertical intercept (graph of football)

The vertical intercept on a graph of a football's flight represents the starting height of the football.

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Horizontal intercept (graph of football)

The horizontal intercept on a graph of a football's flight represents the height when the football hits the ground.

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P(5)

The water depth, in inches, 5 minutes after the pool began filling.

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A(2)

The cost, in dollars, of a 2-mile taxi ride with Company A.

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m when A(m) = B(m)

The distance (in miles) where the cost of a taxi ride for Company A and Company B is the same.

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A(m) > B(m)

The distance (in miles) where Company A's taxi ride cost is greater than Company B's.

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A(m) < B(m)

The distance (in miles) where the cost of a taxi ride with Company A is less than Company B.

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Average rate of change between 1996 and 2004

The average increase in voter participation (18-29 years old) per year between 1996 and 2004, calculated as a difference in voter populations divided by the difference in years.

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Function rule for pool draining

A mathematical formula (p(h) = 100 - 10h) that calculates the remaining water in the pool (p) based on the number of hours (h).

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Equation Solution: p(h) = 20

Solving $p(h) = 100 - 10h = 20$ for 'h' to determine the hours needed for 20 gallons remaining.

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Pool draining rate

The rate at which water drains from a swimming pool, measured in gallons per hour.

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Voter data over 1988-2016

Shows voter turnout data for voters between 18 and 29, recorded yearly during US presidential elections from 1988 to 2016.

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