Average Rate Of Change- It's Really Just The Slope, And We Can Use The Fancy Formula Below, But That's Unnecessary, We Can Just Find Two Coordinate Points
[tex] \frac{g(x + h) - g(x)}{h} [/tex]
X=1
[tex]g(x) = {x}^{2} - \frac{1}{4} \\ g(1) = (1)^{2} - \frac{1}{4} \\ g(1) = \frac{3}{4} \\ (1, \frac{3}{4} )[/tex]
x=3
[tex]g(x) = {x}^{2} - \frac{1}{4} \\ g(3) = (3)^{2} - \frac{1}{4} \\ g(3) = 9 - \frac{1}{4} \\ g(3) = \frac{35}{4} \\ (3, \frac{35}{4} )[/tex]
Slope
[tex] \frac{y_2- y_1}{x_2- x_1} [/tex]
[tex](1, \frac{3}{4} ) \\ (3, \frac{35}{4} ) \: [/tex]
[tex] \frac{ \frac{35}{4} - \frac{3}{4} }{3- 1} \: = \frac{ \frac{32}{4} }{2} = \frac{32}{4} \times \frac{1}{2} = \frac{32}{4} = 8[/tex]
ANSWER
[tex]8 \: avg \: rate \: of \: change \: between \: points[/tex]
