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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 the following problems, 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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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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| 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).
Hint: x – 5 = 4 and x – 5 = –4
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| 17) Given the function y = x2 – 4, state the x-intercept(s) and the y-intercept(s).
Hint: Factor x2 – 4 set each factor equal to zero and solve for x.
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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 following 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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End Behavior
Use the graph to answer the following questions.
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| 23) State the end behavior for this graph as x approaches –∞ (negative infinity).
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| 24) State the end behavior for this graph as x approaches +∞ (positive infinity).
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Use the graph to answer the following questions.
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| 25) State the end behavior for this graph as x approaches –∞.
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| 26) State the end behavior for this graph as x approaches +∞.
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| 27) What is a relative minimum?
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| Study the two functions below. Then, answer the following questions. |
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| 28) Compare f (x) and g(x) and state which one has the lower minimum and what it is.
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| 29) State the intersection points of the two functions.
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| 30) State which function has the larger y-intercept and what it is.
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| 31) 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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| No offline activities found |
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