Range of Rational Functions...2

[nycmathguy]

For f(x) = (2x - 7)/(x^2), find the range algebraically. Also, graph the function and find the range by looking at the graph of f.

 

[MathLover1]

f(x) = (2x - 7)/(x^2)

from the graph you see a highest point (7,1/7)=> range is f(x) <=1/7

Range of :
f(x) = (2x - 7)/x^2
the set of values of the dependent variable for which a function is defined

Rewrite as
y=(2x - 7)/x^2
yx^2=2x - 7
yx^2-2x +7 =0
the range is the set of y for which the discriminant is greater or equal to zero
b^2-4ac>=0
(-2)^2-4y*7>=0
4-28y>=0
4>=28y
y<=4/28
y<=1/7

{f (x) element R : f(x) <= 1/7}

 

[nycmathguy]

f(x) = (2x - 7)/(x^2)

View attachment 491

from the graph you see a highest point (7,1/7)=> range is f(x) <=1/7

Range of :
f(x) = (2x - 7)/x^2
the set of values of the dependent variable for which a function is defined

Rewrite as
y=(2x - 7)/x^2
yx^2=2x - 7
yx^2-2x +7 =0
the range is the set of y for which the discriminant is greater or equal to zero
b^2-4ac>=0
(-2)^2-4y*7>=0
4-28y>=0
4>=28y
y<=4/28
y<=1/7

{f (x) element R : f(x) <= 1/7}

Sorry but I don't follow???