Questions: Evaluate the piecewise function at the given values of the independent variable. f(x)= 2x+3 if x<0 3x+6 if x≥0 (a) f(-2) (b) f(0) (c) f(4)

Transcript text: Evaluate the piecewise function at the given values of the independent variable. \[ f(x)=\left\{\begin{array}{ll} 2 x+3 & \text { if } x<0 \\ 3 x+6 & \text { if } x \geq 0 \end{array}\right. \] (a) $f(-2)$ (b) $f(0)$ (c) $f(4)$

Solution

Solution Steps

Step 1: Identify the Appropriate Piece

Given $x = -2$, we find the condition that it satisfies.

Step 2: Evaluate the Function

The condition satisfied is , thus we evaluate the corresponding function $g(x) = (x)$.

Calculation:

Substituting $x = -2$ into the function, we get $g(-2) = -1$.

Final Answer:

The value of the piecewise function at $x = -2$ is -1.

Step 1: Identify the Appropriate Piece

Given $x = 0$, we find the condition that it satisfies.

Step 2: Evaluate the Function

The condition satisfied is , thus we evaluate the corresponding function $g(x) = (x)$.

Calculation:

Substituting $x = 0$ into the function, we get $g(0) = 6$.

Final Answer:

The value of the piecewise function at $x = 0$ is 6.

Step 1: Identify the Appropriate Piece

Given $x = 4$, we find the condition that it satisfies.

Step 2: Evaluate the Function

The condition satisfied is , thus we evaluate the corresponding function $g(x) = (x)$.

Calculation:

Substituting $x = 4$ into the function, we get $g(4) = 18$.

Final Answer:

The value of the piecewise function at $x = 4$ is 18.

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