Given the function f(x)=x-2m+2 what is m if the graph of the function does not intersect x axis? x>0

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tonys538 | Student, Undergraduate | (Level 1) Valedictorian

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The function f(x)=x-2m+2. The value of x is greater than 0. The graph of the function does not intersect the x axis if for no value of x is the value of f(x) equal to 0.

`x - 2m + 2 != 0`

`x != 2m - 2`

Now as x > 0 , 2m - 2 > 0

or 2m > 2

m > 1

For values of m greater than 1, the graph of f(x)=x-2m+2, x>0 does not intersect the x axis.

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giorgiana1976 | College Teacher | (Level 3) Valedictorian

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If the graph of the function (which is a line) does not intercept the x axis, that means that the equation of the line has no real solutions.

In other words, there are no such values for x to cancel the equation of the line.

When the graph is intercepting x axis, then y = 0.

Let f(x) = y.

Since the graph is not intercepting x axis, then y > 0 =>

x-2m+2 > 0

We'll isolate x to the left side:

x > 2m - 2

Since x > 0 => 2m - 2 > 0

We'll divide by 2:

m - 1 > 0

m > 1

The interval of possible values for m, for the graph of f(x) not to intercept x axis, is: (1 , +infinite).

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