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| 1) What does the graph of a function represent?
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| 2) What do the intersection points of two functions represent?
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For problems #3-7, use the following functions to find the intersection points. You may choose to do this algebraically or graphically.
f (x) = 2x – 5 g(x) = –3x + 1 h(x) = x2 – 3 j(x) = 3x k(x) = |x| + 1
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| 3) Find the intersection point for f (x) and g(x).
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| 4) Find the intersection points for g(x) and h(x).
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| 5) Find the intersection point for g(x) and j(x).
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| 6) Find the intersection point for f (x) and k(x).
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| 7) Find the intersection point for j(x) and k(x).
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Linear vs. Quadratic vs. Exponential Functions
Two investments are increasing in value at different rates. Investment A began with $600 and is represented by the function a(t) = 2t2 + 5t + 100 where t is the number of months invested. Investment B started with $100 and is represented by the function b(t) = 25(1.15)t. Use a table or graph and answer the following questions.
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| 8) Which investment was worth more at the end of 10 months?
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| 9) Which investment was worth more at the end of 35 months?
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| 10) Which function seems to eventually exceed the other and have the greater outputs for large t values?
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Two new companies are making school supplies. Company W has found the following function to represent the number of supplies they sell, W(x) = 28x2, where x is the number of months supplies are sold. Company Q has found the function for their supplies to be Q(x) = 3.5x. Use this information to answer the following questions.
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| 11) Which company sells more supplies after 2 months?
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| 12) Which company sells more supplies after 4 months?
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| 13) Which function seems to eventually exceed the other and have larger values for larger x values?
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| 14) Which function seems to eventually exceed the other and have the greater outputs for large t values?
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Function Features
Finding x-intercepts and y-intercepts
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| 15) What is an x-intercept?
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| 16) Given the graph of the function f (x)= |x – 5| – 4, state x-intercept(s) and y-intercept(s).
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| 17) Given the function y = x2 – 4, state the x-intercept(s) and the y-intercept(s).
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Increasing/Decreasing and Positive/Negative Intervals
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| 18) What does it mean when we say “where a function is positive?"
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Use the graph to answer the next 4 questions.
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| 19) When is the function positive?
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| 20) When is the function negative?
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| 21) When is the function increasing?
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| 22) When is the function decreasing?
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Use the graph to answer the next 4 questions.
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| 23) When is the function positive?
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| 24) When is the function negative?
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| 25) When is the function increasing?
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| 26) When is the function decreasing?
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Trigonometric Functions
Use the graph to answer the next 5 questions. Two points have been highlighted to help you.
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| 27) Find the midline of the graph.
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| 28) Find the amplitude of the graph.
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| 29) Find the period of the graph.
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| 30) Find the relative maximum for the interval –2 < x < 2.
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| 31) Find the relative minimum for the interval 1 < x < 5.
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Use the graph to answer the next 4 questions. When finding period, try to find points that are easy to work with and not just “peaks." Two points are labeled for you.
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| 32) Find the midline of the graph.
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| 33) Find the amplitude of the graph.
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| 34) Find the period of the graph.
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| 35) Find the relative maximum for the interval 1 < x < 3.
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| 36) Find the relative minimum for the interval 2 < x < 4.
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End Behavior
Use the graph to answer the next 2 questions.
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| 37) State the end behavior for this graph as x approaches –∞ (negative infinity).
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| 38) State the end behavior for this graph as x approaches +∞ (positive infinity).
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Use the graph to answer the next 2 questions.
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| 39) State the end behavior for this graph as x approaches –∞.
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| 40) State the end behavior for this graph as x approaches +∞.
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| 41) What is a relative minimum?
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Word Problems
Study the two functions below. Then answer the following 3 questions.
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| 42) Compare f (x) and g(x) and state which one has the lower minimum and what it is.
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| 43) State the intersection points of the two functions.
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| 44) State which function has the larger y-intercept and what it is.
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| 45) Jan’s clothing shop is discontinuing their winter sweaters. Jan is debating whether to discount the sweaters by $5 each week or an additional 10% each week until they are all sold. If the sweaters are originally $45, write a function that gives the difference in price between the two options.
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| 46) A ball is thrown straight up into the air starting at 2 feet with an initial upward velocity of 30 feet per second. Write a function rule that relates the height (in feet) of the ball and the time (in seconds). Note that gravity has an effect on the height with the distance fallen represented by 16t2 where t is time in seconds.
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| 47) Jude is buying a new home. His mortgage payment is $800 per month. He would like to budget an additional 10% for maintenance and emergencies. He must also budget 1% for taxes. Write a function that gives the total amount Jude needs to budget as a function of the number of months he owns his home.
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| 48) If you were directed by your school to complete Offline Activities for this course, please enter the information on the Log Entry form. |
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