CFU A1-A3 Review

Average Rate of Change (AROC) Formula

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

Secant Line

average rate of change of a function, f, over a closed interval [a, b] is the slope of the secant line

Tangent Line

a line that touches a curve once

When is f(x) increasing?

when the input values increase, the output values increase

If a<b…

f(a)<f(b)

When is f(x) decreasing?

when the input values increase, the output values decrease

If a>b…

f(a)>f(b)

When is f(x)>0 (positive)?

when the output values are >0, f(x) is above the x-axis

When is f(x)<0 (negative)?

when the output values are <0, f(x) is below the x-axis

What is the rate of f(x) if the graph is concave up?

increasing

What is the rate of f(x) if the graph is concave down?

decreasing

What is a point of inflection?

the point on a graph where concavity changes

Linear Function

AROC over consecutive equal-length input value intervals can be given by a constant function; 1st different is constant, so the rate of AROC is zero

Quadratic Function

AROC over consecutive equal-length input value intervals can be given by a linear function; 2nd difference is constant, so rate of AROC is constant