The surface area of a cube can be found using the formula A = 6s^2 where A represents the surface area of the cube and s represents the length of one edge. My teacher wants me to draw a cube that has a length of at least 5 inches.

She also wants to know the independent variable
Along with notation to show domain and range

A = 6(5 inches)2
6(25 square inches)
150 sq. inches

Don't understand how to write domain and range

Ah, the domain and range! Don't worry, I'll explain it in a fun way. Think of the domain as the "inputs" and the range as the "outputs".

In this case, the independent variable is the length of one edge, represented by 's'. The domain is the set of possible values for 's' that our teacher wants us to consider. Since she wants a cube with a length of at least 5 inches, our domain can be written as:

Domain: s ≥ 5 inches

Now, let's talk about the range. In this problem, the range represents the possible surface areas (outputs) of the cube, given different values of 's'. Since we only have one fixed value for 's' (5 inches), the range will be a single value.

Range: A = 150 square inches

That's it! Domain: s ≥ 5 inches, and Range: A = 150 square inches. Now you have all the fancy notation to impress your teacher!

The independent variable in this case is the length of the edge of the cube (s). The dependent variable is the surface area of the cube (A), as it depends on the value of the independent variable.

To represent the domain and range, you can use set notation. The domain refers to the values that the independent variable can take, which in this case is the length of the edge of the cube. Since the teacher specified that the length should be at least 5 inches, the domain can be represented as:

Domain (length of the edge): {s | s ≥ 5 inches}

The range refers to the values that the dependent variable can take, which in this case is the surface area of the cube. As the formula for surface area yields a positive value, the range can be represented as:

Range (surface area): {A | A > 0}

When writing the domain and range, we need to consider the possible values for the independent variable (in this case, the length of one edge of the cube) and the resulting values for the dependent variable (in this case, the surface area of the cube).

For the domain, we have to think about the acceptable values for the length of one edge. In this case, your teacher wants you to draw a cube with a length of at least 5 inches. So, the domain can be expressed as:

Domain: s ≥ 5 (inches)

This means that the length of one edge of the cube must be equal to or greater than 5 inches.

For the range, we consider the resulting values for the surface area (A) of the cube. In this case, the formula A = 6s^2 gives us the surface area of the cube. The surface area can never be negative, so the range is:

Range: A ≥ 0 (square inches)

This means that the surface area of the cube must be equal to or greater than 0 square inches, since it represents a physical measurement and cannot have negative values.

So, to summarize:

Domain: s ≥ 5 (inches)
Range: A ≥ 0 (square inches)

clearly, for a physical cube, the sides cannot be zero or negative. So, the domain is all positive real values:

s > 0

So, the range, 6s^2, is also all positive reals,

A > 0

Your teacher has further restricted the domain to

s >= 5
So, the range
6s^2 >= 150

In interval notation, that is
domain: [5,∞)
range: [150,∞)