What kind of test will show that each item in the domain has one and only one item in the range?

Question

answer:__________

Match the items.

The task is to match the lettered items with the correct numbered items. Appearing below is a list of lettered items. Following that is a list of numbered items. Each numbered item is followed by a drop-down. Select the letter in the drop down that best matches the numbered item with the lettered alternatives.

a. A letter or symbol that represents a quantity that can change.

b. A letter or symbol that represents a quantity that does not change.

c. Inputs

d. Outputs

1. Domain

2. Constant

3. Variable

4. Range

Given the function f(x) = x2+ x -1, what is the value of f(2)?
Answer:__________

Which statement is incorrect about functions?

a.
For each item in the domain there is only one item associated with it in the range.

b.
For each item in the range there is only one item associated with it in the domain.

c.
Given the function y= f(x) = 2x +1, when x=1, f(1)=3.

d.
Given the function y=f(x)=x, when x = 2, f(2) = 2.

When the vertical line test shows that there is one and only one range item for each domain item, we call that relationship what?
Answer:__________

Answer 1

1. What kind of test will show that each item in the domain has one and only one item in the range?
   Answer: Vertical Line Test

2. Match the items.

   • 1. Domain → c. Inputs
   • 2. Constant → b. A letter or symbol that represents a quantity that does not change.
   • 3. Variable → a. A letter or symbol that represents a quantity that can change.
   • 4. Range → d. Outputs

3. Given the function f(x) = x^2 + x - 1, what is the value of f(2)?
   To calculate f(2):
   f(2) = (2)^2 + (2) - 1
   f(2) = 4 + 2 - 1
   f(2) = 5
   Answer: 5

4. Which statement is incorrect about functions?
   Answer: b. For each item in the range there is only one item associated with it in the domain.
   (This statement is incorrect because a single range item can correspond to multiple domain items in a non-injective function, whereas the statement is true for injective functions.)

5. When the vertical line test shows that there is one and only one range item for each domain item, we call that relationship what?
   Answer: Function (or more specifically, it indicates that the relationship is a function.)