QuestionRhianna claims different functions can share $x$ -intercepts $(-5,0),(2,0),(6,0)$ , domain $[-5,7]$ , and range $[-4,10]$ . Can you find examples?

Studdy Solution

STEP 1

Assumptions1. The x-intercepts are $(-5,0),(,0)$ , and $(6,0)$ . The domain is $-5 \leq x \leq7$
3. The range is $-4 \leq y \leq10$

STEP 2

We need to understand that the x-intercepts are the points where the function crosses or touches the x-axis, i.e., where $y=0$ .

STEP 3

We also need to understand that the domain of a function is the set of all possible x-values and the range is the set of all possible y-values.

STEP 4

Given the x-intercepts, domain, and range, we can sketch different functions that satisfy these conditions.

STEP 5

First, let's sketch a linear function that passes through the given x-intercepts. We can choose a function such that the line passes through the points $(-5,0),(2,0)$ , and $(,0)$ and stays within the given range $-4 \leq y \leq10$ .

STEP 6

One such function could be $f(x) = -x +2$ for $-5 \leq x \leq$ . This function has the same x-intercepts and fits within the given domain and range.

STEP 7

Next, let's sketch a quadratic function that also passes through the given x-intercepts and stays within the given domain and range.

STEP 8

One such function could be $g(x) = (x+5)(x-2)(x-6)$ for $-5 \leq x \leq7$ . This function also has the same x-intercepts and fits within the given domain and range.

STEP 9

Thus, we have shown that it is possible to draw different functions that have the same x-intercepts and the same domain and range.

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QuestionRhianna claims different functions can share $x$ -intercepts $(-5,0),(2,0),(6,0)$ , domain $[-5,7]$ , and range $[-4,10]$ . Can you find examples?

Studdy Solution

STEP 1

Assumptions1. The x-intercepts are $(-5,0),(,0)$ , and $(6,0)$ . The domain is $-5 \leq x \leq7$
3. The range is $-4 \leq y \leq10$

STEP 2

We need to understand that the x-intercepts are the points where the function crosses or touches the x-axis, i.e., where $y=0$ .

STEP 3

We also need to understand that the domain of a function is the set of all possible x-values and the range is the set of all possible y-values.

STEP 4

Given the x-intercepts, domain, and range, we can sketch different functions that satisfy these conditions.

STEP 5

First, let's sketch a linear function that passes through the given x-intercepts. We can choose a function such that the line passes through the points $(-5,0),(2,0)$ , and $(,0)$ and stays within the given range $-4 \leq y \leq10$ .

STEP 6

One such function could be $f(x) = -x +2$ for $-5 \leq x \leq$ . This function has the same x-intercepts and fits within the given domain and range.

STEP 7

Next, let's sketch a quadratic function that also passes through the given x-intercepts and stays within the given domain and range.

STEP 8

One such function could be $g(x) = (x+5)(x-2)(x-6)$ for $-5 \leq x \leq7$ . This function also has the same x-intercepts and fits within the given domain and range.

STEP 9

Thus, we have shown that it is possible to draw different functions that have the same x-intercepts and the same domain and range.

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QuestionRhianna claims different functions can share xxx-intercepts (−5,0),(2,0),(6,0)(-5,0),(2,0),(6,0)(−5,0),(2,0),(6,0), domain [−5,7][-5,7][−5,7], and range [−4,10][-4,10][−4,10]. Can you find examples?

Studdy Solution

STEP 1

Assumptions1. The x-intercepts are (−5,0),(,0)(-5,0),(,0)(−5,0),(,0), and (6,0)(6,0)(6,0). The domain is −5≤x≤7-5 \leq x \leq7−5≤x≤73. The range is −4≤y≤10-4 \leq y \leq10−4≤y≤10

STEP 2

We need to understand that the x-intercepts are the points where the function crosses or touches the x-axis, i.e., where y=0y=0y=0.

STEP 3

We also need to understand that the domain of a function is the set of all possible x-values and the range is the set of all possible y-values.

STEP 4

Given the x-intercepts, domain, and range, we can sketch different functions that satisfy these conditions.

STEP 5

First, let's sketch a linear function that passes through the given x-intercepts. We can choose a function such that the line passes through the points (−5,0),(2,0)(-5,0),(2,0)(−5,0),(2,0), and (,0)(,0)(,0) and stays within the given range −4≤y≤10-4 \leq y \leq10−4≤y≤10.

STEP 6

One such function could be f(x)=−x+2f(x) = -x +2f(x)=−x+2 for −5≤x≤-5 \leq x \leq−5≤x≤. This function has the same x-intercepts and fits within the given domain and range.

STEP 7

Next, let's sketch a quadratic function that also passes through the given x-intercepts and stays within the given domain and range.

STEP 8

One such function could be g(x)=(x+5)(x−2)(x−6)g(x) = (x+5)(x-2)(x-6)g(x)=(x+5)(x−2)(x−6) for −5≤x≤7-5 \leq x \leq7−5≤x≤7. This function also has the same x-intercepts and fits within the given domain and range.

STEP 9

Thus, we have shown that it is possible to draw different functions that have the same x-intercepts and the same domain and range.

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Start learning now

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

QuestionRhianna claims different functions can share $x$ -intercepts $(-5,0),(2,0),(6,0)$ , domain $[-5,7]$ , and range $[-4,10]$ . Can you find examples?

Assumptions1. The x-intercepts are $(-5,0),(,0)$ , and $(6,0)$ . The domain is $-5 \leq x \leq7$
3. The range is $-4 \leq y \leq10$

We need to understand that the x-intercepts are the points where the function crosses or touches the x-axis, i.e., where $y=0$ .

First, let's sketch a linear function that passes through the given x-intercepts. We can choose a function such that the line passes through the points $(-5,0),(2,0)$ , and $(,0)$ and stays within the given range $-4 \leq y \leq10$ .

One such function could be $f(x) = -x +2$ for $-5 \leq x \leq$ . This function has the same x-intercepts and fits within the given domain and range.

One such function could be $g(x) = (x+5)(x-2)(x-6)$ for $-5 \leq x \leq7$ . This function also has the same x-intercepts and fits within the given domain and range.