Question

I need to determine whether each equation is a function or not a function and explain my reasoning and/or show my work

Answer 1

Answer:

y⁴ = 2x² + 7 (Not a function)

y = -x + 3 (Function)

y = x² + 1 (Function)

y = 3/4 x - 5 (Function)

y² = x + 10 (Not a function)

Explanations:

Note that:

An equation is a function only if there is only one value of y for a corresponding value of x

For y⁴ = 2x² + 7:
`y\text{ = }\sqrt[4]{2x^2+7}`

From the above, we can see that there will be multiple values of y for each vaue of x, therefore, y⁴ = 2x² + 7 is not a function

For y = -x + 3:

This is a linear equation in which each value of x gives a distinct value of y, therefore, it is a function

For y = x² + 1:

This is a quadratic equation in which there are distinct values of y for every value of x. It is a function

`\text{For y = }(3)/(4)x-5`

This is also a linear equation that has distinct values of y for each value of x. It is a function

For y² = x + 10
`y\text{ = }\sqrt[]{x+10}`

This equation has two values of y for each value of x, it is not a function.