Reference no: EM132303063
Functions Assignment Questions -
Q1. Use the vertical line test to determine whether the following relations are functions:
Q2 i) State the domain and range of the following relations:
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a)
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x
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y
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b)
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x
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y
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c)
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x
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y
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-3
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7
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-1
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0
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-2
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-4
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-2
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4
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5
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4
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-1
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-4
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-1
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100
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-2
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2
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0
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-4
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0
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6
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3
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1
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1
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-4
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4
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1
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-1
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6
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2
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-4
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12
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3
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7
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-4
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3
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-4
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ii) Which of the above relations are functions? Justify your response.
Q3. Let f(x) = 3x2 - 5x + 1. Find:
a) f(2) b) f(0) c) f(a) d) f(x+1)
Q4. For each of the following:
a. State the base function.
b. Describe the transformation.
c. State the mapping rule.
d. Graph the transformed function.
e. State the domain and range of the transformed function.
i) f(x) = -2√(x-3) + 5 ii) f(x) = 3(1/(4-2x)) + 1
5. Sketch a graph of a function that has all real numbers in its domain and all real numbers less than or equal to -3 in its range.
6. Sketch a graph of a relation that is not a function and that has all real numbers in its domain and all real numbers less than or equal to -3 in its range.
Q7. Find the inverse of the following functions.
a. f(x) = (5x/2) - 4
b. g(x) = 2x2 - 1
8. Sketch a graph of f-1 given the graph of f below.
Q9. To convert from degrees Fahrenheit to degrees Celsius subtract 32 from the temperature (in Fahrenheit) and then multiply by 5/9.
a. Write a function to express the temperature in degrees Celsius, C, in terms of the temperature in degrees Fahrenheit, F.
b. Find the inverse of this function.
c. Is the inverse a function? Explain how you know.
d. What does the inverse represent?
e. Determine the temperature, in Fahrenheit, at 20oC.
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