Piecewise Functions Calculator

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Example

Created on 2024-06-20Asked by Harper Harris (Solvelet student)

Evaluate the piecewise function

f(x) = \begin{cases} x^2, & \text{if } x < 0 \\ 2x + 1, & \text{if } x \geq 0 \end{cases}

x = -2

and

x = 1

Solution

To evaluate the piecewise function

f(x) = \begin{cases} x^2, & \text{if } x < 0 \\ 2x + 1, & \text{if } x \geq 0 \end{cases}

x = -2

and

x = 1

: 1. For

x = -2

f(-2) = (-2)^2 = 4.

2. For

x = 1

f(1) = 2(1) + 1 = 3.

Therefore,

f(-2) = 4

and

f(1) = 3

. Solved on Solvelet with Basic AI Model

Some of the related questions asked by Jackson Thompson on Solvelet

1. Graph the piecewise function

f(x) = \begin{cases} -x + 2, & \text{if } x < 1 \\ x^2, & \text{if } x \geq 1 \end{cases}

.2. Evaluate the piecewise function

g(x) = \begin{cases} 3x - 1, & \text{if } x \leq 0 \\ 2, & \text{if } 0 < x \leq 2 \\ x^2, & \text{if } x > 2 \end{cases}

x = 3

DefinitionWhich are made up of different expressions for corresponding intervals on the domain for that particular function. These allow to define a function which has different rules in different intervals of the input. For example: ABSOLUTE VALUE FUNCTION f(x)={1x−x 0if x<0if x≥0 LOGIC OF PIECEWISE FUNCTION

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