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:

a)	x	y	b)	x	y	c)	x	y
	-3	7		-1	0		-2	-4
	-2	4		5	4		-1	-4
	-1	100		-2	2		0	-4
	0	6		3	1		1	-4
	4	1		-1	6		2	-4
	12	3		7	-4		3	-4

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 20^oC.