Range of a function f(x)

In summary, the range of a function f(x) is the set of all possible output values that the function can produce for a given set of input values. It is different from the domain, which represents the input values of a function. To find the range, you can use graphing or algebraic methods. A function can have an empty range if there are no output values or if they are not within the range. The range is significant in real-life applications as it represents the possible outcomes or results of a situation.
  • #1
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Homework Statement


Please refer to the image attached. The first part, (i).

Homework Equations


None.

The Attempt at a Solution



My answer is 0 </= x </= 4, but the answer says 0<x<4.
Why are 0 and 4 not included?

Since the domain includes 6, then 0.5(6)+1 =4, 4 should be included right?
 

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  • #2
coconut62 said:

Homework Statement


Please refer to the image attached. The first part, (i).

Homework Equations


None.


The Attempt at a Solution



My answer is 0 </= x </= 4, but the answer says 0<x<4.
Why are 0 and 4 not included?

Since the domain includes 6, then 0.5(6)+1 =4, 4 should be included right?

You are right,0 and 4 are part of the range.
 
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What is the definition of range of a function f(x)?

The range of a function f(x) is the set of all possible output values that the function can produce for a given set of input values. It is also known as the "y-values" of a function.

How is the range of a function f(x) different from the domain?

The domain of a function refers to the set of all input values for which the function is defined, while the range refers to the set of all output values that the function can produce. In other words, the domain represents the input values and the range represents the output values of a function.

How can you find the range of a function f(x)?

To find the range of a function f(x), you can graph the function and observe the y-values or output values. Alternatively, you can also use algebraic methods such as substitution and solving for y in terms of x to determine the range.

Can a function have an empty range?

Yes, a function can have an empty range if there are no output values for a given set of input values. This can happen if the function is undefined for certain input values or if the output values are not within the range of the function.

What is the significance of the range of a function f(x) in real-life applications?

The range of a function is important in real-life applications as it represents the possible outcomes or results of a situation. For example, in economics, the range of a demand function represents the possible prices that consumers are willing to pay for a product. In physics, the range of a projectile motion function represents the maximum height or distance that an object can travel.

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