QuestionAnalyze the function $f$ to find where $f(x)=0$ , $f(x)>0$ , and its domain based on the given points.

Studdy Solution

STEP 1

Assumptions1. The function $f$ is defined by the points given. . The graph of $f$ is continuous and piecewise linear between the points given.
3. The points are listed in order of increasing $x$ -value.

STEP 2

To find the $x$ values where $f(x) =0$ , we look for the points where the $y$ -value is $0$ .

STEP 3

From the list of points, we see that the $y$ -value is $0$ at the points $(8,0)$ , $(-2,0)$ , and $(-12,0)$ .

STEP 4

Therefore, the $x$ values where $f(x) =0$ are $x =8$ , $x = -2$ , and $x = -12$ .

STEP 5

To find the $x$ values where $f(x) >0$ , we look for the intervals where the $y$ -value is greater than $0$ .

STEP 6

From the list of points, we see that the $y$ -value is greater than $0$ between the points $(-12,0)$ and $(-2,0)$ , and after the point $(8,0)$ .

STEP 7

Therefore, the $x$ values where $f(x) >0$ are $-12 < x < -2$ and $< x \leq12$ .

STEP 8

The domain of a function is the set of all possible $x$ values. Since the graph of $f$ is continuous and piecewise linear between the points given, the domain is the interval from the smallest $x$ -value to the largest $x$ -value.

STEP 9

From the list of points, we see that the smallest $x$ -value is $-14$ and the largest $x$ -value is $12$ .

STEP 10

Therefore, the domain of $f$ is $-14 \leq x \leq12$ .

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QuestionAnalyze the function $f$ to find where $f(x)=0$ , $f(x)>0$ , and its domain based on the given points.

Studdy Solution

STEP 1

Assumptions1. The function $f$ is defined by the points given. . The graph of $f$ is continuous and piecewise linear between the points given.
3. The points are listed in order of increasing $x$ -value.

STEP 2

To find the $x$ values where $f(x) =0$ , we look for the points where the $y$ -value is $0$ .

STEP 3

From the list of points, we see that the $y$ -value is $0$ at the points $(8,0)$ , $(-2,0)$ , and $(-12,0)$ .

STEP 4

Therefore, the $x$ values where $f(x) =0$ are $x =8$ , $x = -2$ , and $x = -12$ .

STEP 5

To find the $x$ values where $f(x) >0$ , we look for the intervals where the $y$ -value is greater than $0$ .

STEP 6

From the list of points, we see that the $y$ -value is greater than $0$ between the points $(-12,0)$ and $(-2,0)$ , and after the point $(8,0)$ .

STEP 7

Therefore, the $x$ values where $f(x) >0$ are $-12 < x < -2$ and $< x \leq12$ .

STEP 8

The domain of a function is the set of all possible $x$ values. Since the graph of $f$ is continuous and piecewise linear between the points given, the domain is the interval from the smallest $x$ -value to the largest $x$ -value.

STEP 9

From the list of points, we see that the smallest $x$ -value is $-14$ and the largest $x$ -value is $12$ .

STEP 10

Therefore, the domain of $f$ is $-14 \leq x \leq12$ .

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QuestionAnalyze the function fff to find where f(x)=0f(x)=0f(x)=0, f(x)>0f(x)>0f(x)>0, and its domain based on the given points.

Studdy Solution

STEP 1

Assumptions1. The function fff is defined by the points given. . The graph of fff is continuous and piecewise linear between the points given.3. The points are listed in order of increasing xxx-value.

STEP 2

To find the xxx values where f(x)=0f(x) =0f(x)=0, we look for the points where the yyy-value is 000.

STEP 3

From the list of points, we see that the yyy-value is 000 at the points (8,0)(8,0)(8,0), (−2,0)(-2,0)(−2,0), and (−12,0)(-12,0)(−12,0).

STEP 4

Therefore, the xxx values where f(x)=0f(x) =0f(x)=0 are x=8x =8x=8, x=−2x = -2x=−2, and x=−12x = -12x=−12.

STEP 5

To find the xxx values where f(x)>0f(x) >0f(x)>0, we look for the intervals where the yyy-value is greater than 000.

STEP 6

From the list of points, we see that the yyy-value is greater than 000 between the points (−12,0)(-12,0)(−12,0) and (−2,0)(-2,0)(−2,0), and after the point (8,0)(8,0)(8,0).

STEP 7

Therefore, the xxx values where f(x)>0f(x) >0f(x)>0 are −12<x<−2-12 < x < -2−12<x<−2 and <x≤12 < x \leq12<x≤12.

STEP 8

The domain of a function is the set of all possible xxx values. Since the graph of fff is continuous and piecewise linear between the points given, the domain is the interval from the smallest xxx-value to the largest xxx-value.

STEP 9

From the list of points, we see that the smallest xxx-value is −14-14−14 and the largest xxx-value is 121212.

STEP 10

Therefore, the domain of fff is −14≤x≤12-14 \leq x \leq12−14≤x≤12.

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QuestionAnalyze the function $f$ to find where $f(x)=0$ , $f(x)>0$ , and its domain based on the given points.

Assumptions1. The function $f$ is defined by the points given. . The graph of $f$ is continuous and piecewise linear between the points given.
3. The points are listed in order of increasing $x$ -value.

To find the $x$ values where $f(x) =0$ , we look for the points where the $y$ -value is $0$ .

From the list of points, we see that the $y$ -value is $0$ at the points $(8,0)$ , $(-2,0)$ , and $(-12,0)$ .

Therefore, the $x$ values where $f(x) =0$ are $x =8$ , $x = -2$ , and $x = -12$ .

To find the $x$ values where $f(x) >0$ , we look for the intervals where the $y$ -value is greater than $0$ .

From the list of points, we see that the $y$ -value is greater than $0$ between the points $(-12,0)$ and $(-2,0)$ , and after the point $(8,0)$ .

Therefore, the $x$ values where $f(x) >0$ are $-12 < x < -2$ and $< x \leq12$ .

The domain of a function is the set of all possible $x$ values. Since the graph of $f$ is continuous and piecewise linear between the points given, the domain is the interval from the smallest $x$ -value to the largest $x$ -value.

From the list of points, we see that the smallest $x$ -value is $-14$ and the largest $x$ -value is $12$ .

Therefore, the domain of $f$ is $-14 \leq x \leq12$ .