Sketching a graph that meets given condition

• The Subject
In summary, the problem asks for a function f that is defined on [0,1] and has certain conditions. The solutions manual states that it is impossible to meet these conditions. However, whether or not it is possible depends on the interpretation of the conditions.

Homework Statement

Sketch the graph of a function f that is defined on [0,1] and meets the given conditions (if possible)

- f is continuous on (0,1), takes on only two distinct values.

The Attempt at a Solution

https://scontent-lga3-1.xx.fbcdn.net/v/t34.0-12/13020084_1115236431831934_1952173744_n.jpg?oh=36c9b39d36f9d87dbfe189161ecdf210&oe=570FDD68

The solutions manual said it is impossible.

What is wrong with this function?

The Subject said:

Homework Statement

Sketch the graph of a function f that is defined on [0,1] and meets the given conditions (if possible)

- f is continuous on (0,1), takes on only two distinct values.

The Attempt at a Solution

[ IMG]https://scontent-lga3-1.xx.fbcdn.net/v/t34.0-12/13020084_1115236431831934_1952173744_n.jpg?oh=36c9b39d36f9d87dbfe189161ecdf210&oe=570FDD68[/PLAIN]

The solutions manual said it is impossible.

What is wrong with this function?
Is it continuous on (0,1) ?

So, intuitively no, since "i lifted my pen while drawing this function".

(i) the function f is defined at a
Yes

(ii) the limit of f as x approaches a from the right-hand and left-hand limits exist and are equal
If a is the point that jumps, is the lim x-> a = 1 (correct?)

(iii) the limit of f as x approaches a is equal to f(a).
Iim x-> a = 1 does not equal f(a)=2, no

I see

A continuous function on an interval(in R), should possesses an intermediate value property. That's why it's impossible

The Subject said:

Homework Statement

Sketch the graph of a function f that is defined on [0,1] and meets the given conditions (if possible)

- f is continuous on (0,1), takes on only two distinct values.The solutions manual said it is impossible.

Whether or not it is possible depends on exactly how the problem's wording is interpreted.
Interpretation (1): f is defined on [0,1] and takes two values on that set. It is continuous on (0,1).
Interpretation (2): f is defined on [0,1]. It is continuous on (0,1) and takes two values on that set.

Interpretation (1) is possible, but Interpretation (2) is impossible, for reasons explained already by others.

What is the purpose of sketching a graph that meets a given condition?

The purpose of sketching a graph that meets a given condition is to visually represent the relationship between two variables and to demonstrate how one variable changes in relation to the other.

What is the first step in sketching a graph?

The first step in sketching a graph is to determine the type of relationship between the two variables, whether it is linear, quadratic, exponential, etc.

What are some common conditions that may need to be met when sketching a graph?

Some common conditions that may need to be met when sketching a graph include the direction of the relationship (increasing or decreasing), the intercepts of the graph, and the general shape of the graph.

How do you label the axes on a graph?

The horizontal axis (x-axis) should represent the independent variable and the vertical axis (y-axis) should represent the dependent variable. Both axes should also be labeled with the corresponding units of measurement.

What should be included in the title of the graph?

The title of the graph should include both variables and the type of relationship between them, if applicable. It should also be clear and concise.