A graph shows the equation `y^4=x`. At how many points does `x=4` ?

embizze | High School Teacher | (Level 1) Educator Emeritus

Posted on

Given `y^4=x` :

(1) If this is a function:

Rewrite in function form `y=f(x)=x^(1/4)` . The domain of this function is `x>=0` .

A. Since it is a function, there is only one value for x=4 which is `4^(1/4)=sqrt(2)~~1.414`

B. The domain is `x>=0` so there are no values for x=-4.

The graph:

(2) If this is not a function, then:

A. `y^4=4==>y=+-sqrt(2)`

B. There are no values where `y^4=4` in the cartesian plane

The graph of the relation:

** Note that there are complex solutions to both `y^4=4,y^4=-4` , but they will not show up on the graph

jeew-m | College Teacher | (Level 1) Educator Emeritus

Posted on

Since the editors are allowed to answer one question at a time i will only answer the first part.

`y^4 = x`

In the definition of a standard function with direct variable x and depending variable y , the depending variable(y) can only is co-related with only one point in the direct variable(x). Otherwise it cannot be a function.

According to the standard notations in this function y is dependable and x is direct variable.

So for one x value we can have only one y value. But we can have several x values for one y value.

So there will be one y value for x=4.It is y=1.414

and

since `y^4gt=0` there cant be x values which are negative.

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