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Section 1
Relations and Functions
Explain why $\left\{(x, y) : x=y^{2}\right\}$ is not a function but $\{(x, y) : \sqrt{x}=y\}$ is a function.
Can $y=\sqrt{x}$ define a function from the set of positive integers to the set of positive integers? Explain why or why not.
In $3-5 :$ a. Explain why each set of ordered pairs is or is not a function. b. List the elements of the domain. c. List the clements of the range. $$\{(1,1),(2,4),(3,9),(4,16)\}$$
In $3-5 :$ a. Explain why each set of ordered pairs is or is not a function. b. List the elements of the domain. c. List the clements of the range. $$\{(1,-1),(0,0),(1,1)\}$$
In $3-5 :$ a. Explain why each set of ordered pairs is or is not a function. b. List the elements of the domain. c. List the clements of the range. $$\{(-2,5),(-1,5),(0,5),(1,5),(2,5)\}$$
In $6-11 :$ a. Determine whether or not each graph represents a function. b. Find the domain for each graph. c. Find the range for each graph.
In $12-23,$ each set is a function from set $A$ to set $B .$ a. What is the largest subset of the real numbers that can be set $A$ , the domain of the given function? b. If set $A=\operatorname{set} B,$ is the function onto? Justify your answer. $$\{(x, y) : y=-183\}$$
In $12-23,$ each set is a function from set $A$ to set $B .$ a. What is the largest subset of the real numbers that can be set $A$ , the domain of the given function? b. If set $A=\operatorname{set} B,$ is the function onto? Justify your answer. $$\{(x, y) : y=5-x\}$$
In $12-23,$ each set is a function from set $A$ to set $B .$ a. What is the largest subset of the real numbers that can be set $A$ , the domain of the given function? b. If set $A=\operatorname{set} B,$ is the function onto? Justify your answer. $$\left\{(x, y) : y=x^{2}\right\}$$
In $12-23,$ each set is a function from set $A$ to set $B .$ a. What is the largest subset of the real numbers that can be set $A$ , the domain of the given function? b. If set $A=\operatorname{set} B,$ is the function onto? Justify your answer. $$\left\{(x, y) : y=-x^{2}+3 x-2\right\}$$
In $12-23,$ each set is a function from set $A$ to set $B .$ a. What is the largest subset of the real numbers that can be set $A$ , the domain of the given function? b. If set $A=\operatorname{set} B,$ is the function onto? Justify your answer. $$\{(x, y) : y=\sqrt{2 x}\}$$
In $12-23,$ each set is a function from set $A$ to set $B .$ a. What is the largest subset of the real numbers that can be set $A$ , the domain of the given function? b. If set $A=\operatorname{set} B,$ is the function onto? Justify your answer. $$\{(x, y) : y=|4-x|\}$$
In $12-23,$ each set is a function from set $A$ to set $B .$ a. What is the largest subset of the real numbers that can be set $A$ , the domain of the given function? b. If set $A=\operatorname{set} B,$ is the function onto? Justify your answer. $$\left\{(x, y) : y=\frac{1}{x}\right\}$$
In $12-23,$ each set is a function from set $A$ to set $B .$ a. What is the largest subset of the real numbers that can be set $A$ , the domain of the given function? b. If set $A=\operatorname{set} B,$ is the function onto? Justify your answer. $$\{(x, y) : y=\sqrt{3-x}\}$$
In $12-23,$ each set is a function from set $A$ to set $B .$ a. What is the largest subset of the real numbers that can be set $A$ , the domain of the given function? b. If set $A=\operatorname{set} B,$ is the function onto? Justify your answer. $$\left\{(x, y) : y=\frac{1}{\sqrt{x+1}}\right\}$$
In $12-23,$ each set is a function from set $A$ to set $B .$ a. What is the largest subset of the real numbers that can be set $A$ , the domain of the given function? b. If set $A=\operatorname{set} B,$ is the function onto? Justify your answer. $$\left\{(x, y) : y=\frac{1}{x^{2}+1}\right\}$$
In $12-23,$ each set is a function from set $A$ to set $B .$ a. What is the largest subset of the real numbers that can be set $A$ , the domain of the given function? b. If set $A=\operatorname{set} B,$ is the function onto? Justify your answer. $$\left\{(x, y) : y=\frac{x+1}{x-1}\right\}$$
In $12-23,$ each set is a function from set $A$ to set $B .$ a. What is the largest subset of the real numbers that can be set $A$ , the domain of the given function? b. If set $A=\operatorname{set} B,$ is the function onto? Justify your answer. $$\left\{(x, y) : y=\frac{x-5}{|x-3|}\right\}$$
The perimeter of a rectangle is 12 meters.a. If $x$ is the length of the rectangle and $y$ is the area, describe, in set-builder notation, the area as a function of length.b. Use integral values of $x$ from 0 to 10 and find the corresponding values of $y .$ Sketch the graph of the function.c. What is the largest subset of the real numbers that can be the domain of the function?
A candy store sells candy by the piece for 10 cents each. The amount that a customer pays for candy, $y,$ is a function of the number of pieces purchased, $x .$ a. Describe, in set-builder notation, the cost in cents of each purchase as a function of the number of pieces of candy purchased.b. Yesterday, no customer purchased more than 8 pieces of candy. List the ordered pairs that describe possible purchases yesterday.c. What is the domain for yesterday's purchases?d. What is the range for yesterday's purchases?