Which of these relations are functions of x on R

In summary, the conversation discusses the trigonometric functions of sine, cosine, tangent, cosecant, secant, and cotangent. The question is about determining the value of x that makes all the functions pass the vertical line test, and the answer is that only sine and cosine have a domain of all real numbers, while the others are undefined at the x coordinate of the vertical asymptote.
  • #1
Erenjaeger
141
6
Mentor note: moved to homework section

y = sin(x)
y = cos(x)
y = tan(x)
y = csc(x)
y = sec(x)
y = cot(x)

(a) 0 (b) 4 (c) 6 (d) 2
I thought it was (c) because i graphed all the trig functions and they passed the vertical line test but the answer sheet is saying (d) 2
 
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  • #2
"on R" is referring to the domain of function being all real numbers. Only sine and cosine satisfy this.
 
  • #3
pwsnafu said:
"on R" is referring to the domain of function being all real numbers. Only sine and cosine satisfy this.
oh true, that's where i was confused i think then, so is that because the others have vertical asymptotes ?
 
  • #4
no, it is because they are not defined at the x coordinate of the vertical asymptote. but i think that is what you meant.
 
  • #5
mathwonk said:
no, it is because they are not defined at the x coordinate of the vertical asymptote. but i think that is what you meant.
yeah that's what i was meaning, thanks
 

1. What is the definition of a function in relation to x on R?

A function is a mathematical concept that describes the relationship between two sets of values, typically represented by the variables x and y. In the context of x on R, a function is defined as a relation where each input value of x corresponds to exactly one output value on the set of real numbers, R.

2. How can you determine if a relation is a function of x on R?

To determine if a relation is a function of x on R, you can use the Vertical Line Test. If a vertical line can be drawn through any point on the graph of the relation and only intersects the graph at one point, then the relation is a function of x on R.

3. What is the difference between a one-to-one function and a many-to-one function?

A one-to-one function, also known as an injective function, is a function where each input value of x corresponds to a unique output value. In other words, no two input values can have the same output value. On the other hand, a many-to-one function, also known as a non-injective function, is a function where multiple input values can have the same output value.

4. Can a relation be a function of x on R if it has multiple output values for the same input value?

No, a relation cannot be a function of x on R if it has multiple output values for the same input value. This violates the definition of a function, which states that each input value must correspond to exactly one output value.

5. What is the domain and range of a function of x on R?

The domain of a function of x on R is the set of all possible input values, which in this case is the set of real numbers, R. The range of a function of x on R is the set of all possible output values, which can be determined by looking at the graph of the function or by finding the solution set of the function's equation.

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