QuestionEvaluate $f(0)$ and $f(6)$ for the piecewise function: $f(x)=\{2x, -2 \leq x \leq 3; 4, 3 < x \leq 5\}$ . Graph $f$ .

Studdy Solution

STEP 1

Assumptions1. The function $f(x)$ is defined as a piecewise function with two parts. . The first part of the function, $x$ , is applicable for $- \leq x \leq3$ .
3. The second part of the function, $4$ , is applicable for $3 < x \leq5$ .

STEP 2

To evaluate $f(0)$ , we need to determine which part of the piecewise function to use. Since $0$ falls in the range $-2 \leq x \leq$ , we use the first part of the function.
$f(0) =2 \times0$

STEP 3

Calculate the value of $f(0)$ .
$f(0) =2 \times0 =0$ So, $f(0) =0$ .

STEP 4

To evaluate $f(6)$ , we need to determine which part of the piecewise function to use. Since $6$ does not fall in the range of either $-2 \leq x \leq3$ or $3 < x \leq$ , $f(6)$ is undefined.

STEP 5

To graph the function $f(x)$ , we need to graph each part of the piecewise function separately.For the first part, $2x$ , we graph a line with slope $2$ and y-intercept $0$ from $x=-2$ to $x=3$ . This line will be a straight line passing through the points $(-2, -4)$ , $(0,0)$ , and $(3,)$ .
For the second part, $4$ , we graph a horizontal line at $y=4$ from $x=3$ to $x=5$ . This line will be a straight line passing through the points $(3,4)$ and $(5,4)$ .
Note The point at $x=3$ should be an open circle on the line $y=4$ and a closed circle on the line $2x$ to indicate that $f(3)$ is defined by the first part of the function, not the second part.

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