Question

Is the parabola $y=x^2$a function? Is the parabola

$x=y^2$a function? Explain why or why not.

Short answer

The parabola $y=x^2$is not a function since it is not one-to-one function and does not hold the horizontal line test and the parabola $x=y^2$is not a function since it is not one-to-one function and does not hold the vertical line test.

Step-by-step solution

Step 1. Define function.

A function is a mathematical expression that expresses the relationship between the independent and dependent variables which shows the relationship between a set of inputs and a set of possible outputs where each input corresponds to one output.

Step 3. Describe whether the given parabola y=x2 and x=y2 are function .

In parabola, $y=x^2$, $x$is dependent variable and $y$is independent variable.

The parabola $y=x^2$is not a function since it is not one-to-one function and does not hold the horizontal line test.

In parabola, $x=y^2$, $y$is dependent variable and $x$is independent variable.

The parabola $x=y^2$is not a function since it is not one-to-one function and does not hold the vertical line test.