Final Exam Formulas & Example Problems MATH115

ARoC (Average Rate of Change) Formula

f(b) - f(a)/ b-a

Find the average rate of change of the function. f(x) = 3x +7 between x = -1 and x = 2.

f(a) = 4, f(b) = 13, ARoC = 3

Solve 7x-11< 2(x-3). Write as an interval and graph.

x<1, (-∞,1)

Solve -1≤ 3x+11≤14

-4≤x≤1, [-4,1]

Absolute Value is finding what?

the distance from zero

|u| < a

-a < u < a

|u| ≤ a

-a ≤ u ≤ a

|u| > a

u > a or u < -a

|u| ≥ a

u ≥ a or u ≤ -a

Solve |3x-2| > -5 (possibilities and answers)

3x -2 > 5 or 3x -2 < 5 (x<7/3, x>-1)

f(x+h)

horizontal. shift left by h units

f (x-h)

horizontal shift right by h units

f(x) + k

vertical shift upward by k units

f(x) - k

vertical shift downward by k units

a × f(x) when a > 1

vertical stretch by a units

a × f(x) when a < 0

reflects across the x-axis

a × f(x) when 0 < a < 1

vertical compression by a units

(fog)(x) is also…

f (g(x))

(gof) (x) is also…

g(f(x))