QuestionFind $f(6)$ for the piecewise function: $f(x)=\{2x \text{ if } -2 \leq x \leq 3; 4 \text{ if } 3<x \leq 5\}$ .

Studdy Solution

STEP 1

Assumptions1. The function $f(x)$ is defined as a piecewise function, with two different rules for different ranges of $x$ . . We need to evaluate $f(6)$ and graph the function $f(x)$ .

STEP 2

We first need to determine which rule to use when evaluating $f(6)$ . To do this, we need to see which range $x =6$ falls into.
The ranges given are $-2 \leq x \leq$ and $< x \leq5$ .

STEP 3

We can see that $x =6$ does not fall into either of the given ranges. Therefore, $f(6)$ is undefined.

STEP 4

Now, let's move on to graphing the function $f(x)$ . The first part of the function is $2x$ for $-2 \leq x \leq3$ . This is a straight line with a slope of2 and it includes the points where $x = -2$ and $x =3$ .

STEP 5

The second part of the function is a constant $4$ for $3 < x \leq5$ . This is a horizontal line at $y =4$ , and it includes the point where $x =5$ but does not include the point where $x =3$ (since $3 < x$ ).

STEP 6

Putting these two parts together, we can draw the graph of the function $f(x)$ .

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QuestionFind $f(6)$ for the piecewise function: $f(x)=\{2x \text{ if } -2 \leq x \leq 3; 4 \text{ if } 3<x \leq 5\}$ .

Studdy Solution

STEP 1

Assumptions1. The function $f(x)$ is defined as a piecewise function, with two different rules for different ranges of $x$ . . We need to evaluate $f(6)$ and graph the function $f(x)$ .

STEP 2

We first need to determine which rule to use when evaluating $f(6)$ . To do this, we need to see which range $x =6$ falls into.
The ranges given are $-2 \leq x \leq$ and $< x \leq5$ .

STEP 3

We can see that $x =6$ does not fall into either of the given ranges. Therefore, $f(6)$ is undefined.

STEP 4

Now, let's move on to graphing the function $f(x)$ . The first part of the function is $2x$ for $-2 \leq x \leq3$ . This is a straight line with a slope of2 and it includes the points where $x = -2$ and $x =3$ .

STEP 5

The second part of the function is a constant $4$ for $3 < x \leq5$ . This is a horizontal line at $y =4$ , and it includes the point where $x =5$ but does not include the point where $x =3$ (since $3 < x$ ).

STEP 6

Putting these two parts together, we can draw the graph of the function $f(x)$ .

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QuestionFind f(6)f(6)f(6) for the piecewise function: f(x)={2x if −2≤x≤3;4 if 3<x≤5}f(x)=\{2x \text{ if } -2 \leq x \leq 3; 4 \text{ if } 3<x \leq 5\}f(x)={2x if −2≤x≤3;4 if 3<x≤5}.

Studdy Solution

STEP 1

Assumptions1. The function f(x)f(x)f(x) is defined as a piecewise function, with two different rules for different ranges of xxx. . We need to evaluate f(6)f(6)f(6) and graph the function f(x)f(x)f(x).

STEP 2

We first need to determine which rule to use when evaluating f(6)f(6)f(6). To do this, we need to see which range x=6x =6x=6 falls into.The ranges given are −2≤x≤-2 \leq x \leq−2≤x≤ and <x≤5 < x \leq5<x≤5.

STEP 3

We can see that x=6x =6x=6 does not fall into either of the given ranges. Therefore, f(6)f(6)f(6) is undefined.

STEP 4

Now, let's move on to graphing the function f(x)f(x)f(x). The first part of the function is 2x2x2x for −2≤x≤3-2 \leq x \leq3−2≤x≤3. This is a straight line with a slope of2 and it includes the points where x=−2x = -2x=−2 and x=3x =3x=3.

STEP 5

The second part of the function is a constant 444 for 3<x≤53 < x \leq53<x≤5. This is a horizontal line at y=4y =4y=4, and it includes the point where x=5x =5x=5 but does not include the point where x=3x =3x=3 (since 3<x3 < x3<x).

STEP 6

Putting these two parts together, we can draw the graph of the function f(x)f(x)f(x).

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Studdy solves anything!

Start learning now

Download Studdy AI Tutor now. Learn with ease and get all help you need to be successful at school.

QuestionFind $f(6)$ for the piecewise function: $f(x)=\{2x \text{ if } -2 \leq x \leq 3; 4 \text{ if } 3<x \leq 5\}$ .

Assumptions1. The function $f(x)$ is defined as a piecewise function, with two different rules for different ranges of $x$ . . We need to evaluate $f(6)$ and graph the function $f(x)$ .

We first need to determine which rule to use when evaluating $f(6)$ . To do this, we need to see which range $x =6$ falls into.
The ranges given are $-2 \leq x \leq$ and $< x \leq5$ .

We can see that $x =6$ does not fall into either of the given ranges. Therefore, $f(6)$ is undefined.

Now, let's move on to graphing the function $f(x)$ . The first part of the function is $2x$ for $-2 \leq x \leq3$ . This is a straight line with a slope of2 and it includes the points where $x = -2$ and $x =3$ .

The second part of the function is a constant $4$ for $3 < x \leq5$ . This is a horizontal line at $y =4$ , and it includes the point where $x =5$ but does not include the point where $x =3$ (since $3 < x$ ).

Putting these two parts together, we can draw the graph of the function $f(x)$ .