MHF 4U1- ASSIGNMENT CHAPTER 3 B
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University of Toledo *
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MISC
Subject
Mathematics
Date
Nov 24, 2024
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4
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MHF 4U1- ASSIGNMENT CHAPTER 3 B NAME:________________________
True/False
Indicate whether the statement is true or false.
____ 1. The solution to is .
____ 2. The solution to is .
Multiple Choice
Identify the choice that best completes the statement or answers the question.
____ 3. Solve the equation . a.
x
= –
1 c.
x
= –
5 b.
x
= 5 d.
no solution ____ 4. Solve the equation . a.
x
= 2 c.
x
= –
2 b.
x
= d.
no solution ____ 5. What are the x
-intercepts of the graph of ? a.
–
4, 5 c.
4, –
5 b.
–
7, 3 d.
7, –
3 ____ 6. For what values of k
does the graph of have no x
-intercepts? a.
c.
b.
d.
____ 7. Which of the following rational equations requires the use of technology to solve? a.
c.
b.
d.
____ 8. Which of the following rational inequalities requires the use of technology to solve? a.
c.
b.
d.
____ 9. Use the graph of to solve the equation . a.
c.
b.
d.
no solution ____ 10. Use the graph of to solve the inequality . a.
c.
b.
d.
no solution
Short Answer
11. Solve. a)
b)
c)
d)
12. Solve each equation by graphing, using technology. Express your answers to two decimal places. a)
b)
c)
d)
13. Solve each inequality by graphing, using technology. Express your answers to one decimal place. a)
b)
c)
d)
Problem
14. A photographer uses a light meter to measure the intensity of light from a flash bulb. The intensity for the flash bulb, I
, in lux, is a function of the distance from the light, d
, in metres, and can be represented by . a) Determine the following, to two decimal places. i)
the intensity of light 3 m from the flash bulb ii)
the average rate of change in the intensity of light for the interval iii)
the approximate instantaneous rate of change in the intensity of light at exactly 3 m from the flash bulb b)
What does the sign of your answer to part a), subpart iii), indicate about the light intensity?
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15. Ingrid is docking a motorboat. She turns off the power and lets the boat coast toward the dock. The distance, d
, in metres, between the boat and the dock as a function of time, t
, in seconds, is given by . a)
What is the average velocity of the boat during the time interval from when Ingrid turns the boat off to when it meets the dock? b)
Determine the velocity of the boat when Ingrid turns off the power, to one decimal place. c) Determine the velocity of the boat when it meets the dock, to one decimal place. d)
Sketch a graph of the function. On the same set of axes, sketch a graph of the speed
of the boat in relation to the time.
16. Write an equation for the graph of the rational function shown. Explain your reasoning. 17. Determine an equation in the form for a function that has asymptotes with equations and and a y
-intercept of 2. Sketch a graph of your function.
18. Explain the difference between the solution to the equation and the solution to .
19. Write an equation for a rational function whose graph has all of the indicated features. • vertical asymptote with equation x
= 3 • horizontal asymptote with equation y
= 2 • hole at x
= 1 • no x
-intercepts 20. a)
Use the asymptotes and intercepts to make a quick sketch of the function and its reciprocal, , on the same set of axes. b)
Describe the symmetry in the graphs in part a). c)
Determine the equation of the mirror line in your graph from part a). d)
Determine intervals of increase and decrease for both f
and f
R
. How do the sets of intervals compare? e)
Would the pattern from part d) occur for all pairs of functions and ? Explain why or why not