Hi,

My equation is 4x^2-8. I think the independent variable for the equation is 4 and the dependent is x. Is that right? I also have to find the domain and range but I'm not sure how to find those for this equation.

you stated "My equation is 4x^2-8" but

4x^2 - 8 is not an equation.
Did you mean
y = 4x^2 - 8x or f(x) = 4x^2 - 8x ?

If so , then x is the independent variable and y or f(x) is the dependent variable, because the value of y "depends" on what you choose for the x.

The graph of your function will be a parabola which opens upwards and has a vertex at (0,-8)
You could find that by making a table of values and graphing it.
You will see that the domain, your choices for x, is the set of real numbers while the range, the resulting y values, are the set of real number, y ≥ -8

Sorry, I meant that the equation is z=4x^2-8. I forgot to add the z if that makes a difference.

Then you are all set. The answer Reiny gave you applies. Either z or y or f(x) is fine on the left.

Okay, thank you.

Hi there!

To correctly identify the independent and dependent variables in an equation, it's important to understand their roles.

In your equation, 4x^2 - 8, it seems like you might have a small misunderstanding. An independent variable is typically denoted by a letter, such as x, while the dependent variable is the result of the equation and depends on the value of the independent variable.

In this case, x is actually the independent variable, as it can take on various values. For each value of x, you can calculate the corresponding value of the equation. For example, if x = 2, plugging it into the equation gives you 4(2)^2 - 8 = 4(4) - 8 = 16 - 8 = 8.

So, x can be any real number, and as you plug in different values for x, you'll obtain different outputs for the equation.

Now, let's move on to the domain and range of the equation. The domain refers to the set of all possible values that the independent variable, x, can take on. In this case, since x can be any real number, the domain is the set of all real numbers, often expressed as (-∞, ∞).

As for the range, it represents the set of all possible outputs or values that the dependent variable, the equation itself, can have. In this case, since the equation is a quadratic expression (4x^2 - 8), it opens upward (positive leading coefficient), which means the lowest value it can have is the vertex (if it exists). Since we don't have enough information to determine the vertex, we can say that the range of the equation is from negative infinity to positive infinity, or (-∞, ∞).

I hope this explanation clarifies things for you! Let me know if there's anything else I can help you with.