Graphs of Functions - Red Bank Regional High School

Section 1.3

Graphs of Functions

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Do Now

Evaluate the function at each specified value of the independent variable and simplify. f(x) = 2 + 3x - x2 a. f(-3) b. f(x+1) c. f(x+h) - f(x)

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Do Now

f(x) = 2 + 3x - x2 a. f(-3) = 2 + 3(-3) - (-3)2 = 2 - 9 - 9 = -16

b. f(x+1) = 2 + 3(x+1) - (x+1)2 = 2 + 3x + 3 - [x2 + 2x + 1] = -x2 + x + 4

c. f(x+h) - f(x) = 2 + 3(x+h) - (x+h)2 - [2 + 3x - x2] = 2 + 3x + 3h - [x2 + 2xh + h2] - 2 - 3x + x2 = 2 + 3x + 3h - x2 - 2xh - h2 - 2 - 3x + x2 = 3h - 2xh - h2

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Domain and Range

The set of all possible inputs (x-values) of a function is called the domain of a function.

The set of all the possible outputs (y-values) of a function is called the range of a function.

If I have the function f(x) = x2,

-The domain would be all real numbers because any input is acceptable, D: (-, )

x-value

-The range would be all nonnegative numbers because there are no negative y-value outputs.

-Zero is included because (0, 0) is a point on the curve. R: [0, ). 4

Graphs of Functions

State the domain and range in interval notation. Then find f(0).

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2.

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Graphs of Functions

State the domain and range in interval notation. Then find f(0).

1.

2.

D: (-, ); R: (-, 4]; f(0) = 3

D: [-5, 5]; R: [-4, 4]; f(0) = 4

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Increasing, Decreasing, and Constant Functions

A function f is increasing on an interval if, for any x1 and x2 in the interval, x1 < x2 implies f(x1) < f(x2).

A function f is decreasing on an interval if, for any x1 and x2 in the interval, x1 < x2 implies f(x1) > f(x2).

A function f is constant on an interval if, for any x1 and x2 in the interval, f(x1) = f(x2).

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Increasing, Decreasing, and Constant Functions

Increasing

Decreasing

Constant

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