Math / Algebra

Questionس ۲ + ٥ س - ٦ ، رس - ٥٦ - 7- دا مثال : أُمثلُ بيانياً الاقتران ق (س) - - (س + هس - ٦ ، ٦٠ س ١ = س" + ٥س – ٦ ، س ۱۷ C

Studdy Solution

STEP 1

1. The function $ق(س)$ is a piecewise function with three different expressions based on the value of $س$ .
2. We need to graph each piece of the function separately according to its domain.

STEP 2

1. Identify the expressions and their respective domains.
2. Graph each piece of the function over its domain.
3. Combine the graphs to represent the entire piecewise function.

STEP 3

Identify the expressions and their domains: - $ق(س) = س^2 + 2س - 6$ for $س \geq 6$ - $ق(س) = -(س^2 + 3س - 6)$ for $1 < س < 6$ - $ق(س) = س - 2$ for $س \leq 1$

STEP 4

Graph the first piece $ق(س) = س^2 + 2س - 6$ for $س \geq 6$ : - This is a quadratic function opening upwards. - Plot the graph starting from $س = 6$ and extending to the right.

STEP 5

Graph the second piece $ق(س) = -(س^2 + 3س - 6)$ for $1 < س < 6$ : - This is a quadratic function opening downwards. - Plot the graph between $س = 1$ and $س = 6$ .

STEP 6

Graph the third piece $ق(س) = س - 2$ for $س \leq 1$ : - This is a linear function with a slope of 1. - Plot the graph starting from $س = 1$ and extending to the left.

STEP 7

Combine the graphs from each step to form the complete piecewise function. - Ensure continuity or discontinuity at the boundaries $س = 1$ and $س = 6$ as per the domain restrictions.
The graph of the piecewise function $ق(س)$ is now complete.

Was this helpful?

Questionس ۲ + ٥ س - ٦ ، رس - ٥٦ - 7- دا مثال : أُمثلُ بيانياً الاقتران ق (س) - - (س + هس - ٦ ، ٦٠ س ١ = س" + ٥س – ٦ ، س ۱۷ C

Studdy Solution

STEP 1

1. The function $ق(س)$ is a piecewise function with three different expressions based on the value of $س$ .
2. We need to graph each piece of the function separately according to its domain.

STEP 2

1. Identify the expressions and their respective domains.
2. Graph each piece of the function over its domain.
3. Combine the graphs to represent the entire piecewise function.

STEP 3

Identify the expressions and their domains: - $ق(س) = س^2 + 2س - 6$ for $س \geq 6$ - $ق(س) = -(س^2 + 3س - 6)$ for $1 < س < 6$ - $ق(س) = س - 2$ for $س \leq 1$

STEP 4

Graph the first piece $ق(س) = س^2 + 2س - 6$ for $س \geq 6$ : - This is a quadratic function opening upwards. - Plot the graph starting from $س = 6$ and extending to the right.

STEP 5

Graph the second piece $ق(س) = -(س^2 + 3س - 6)$ for $1 < س < 6$ : - This is a quadratic function opening downwards. - Plot the graph between $س = 1$ and $س = 6$ .

STEP 6

Graph the third piece $ق(س) = س - 2$ for $س \leq 1$ : - This is a linear function with a slope of 1. - Plot the graph starting from $س = 1$ and extending to the left.

STEP 7

Combine the graphs from each step to form the complete piecewise function. - Ensure continuity or discontinuity at the boundaries $س = 1$ and $س = 6$ as per the domain restrictions.
The graph of the piecewise function $ق(س)$ is now complete.

Get Studdy

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.

Questionس ۲ + ٥ س - ٦ ، رس - ٥٦ - 7- دا مثال : أُمثلُ بيانياً الاقتران ق (س) - - (س + هس - ٦ ، ٦٠ س ١ = س" + ٥س – ٦ ، س ۱۷ C

Studdy Solution

STEP 1

1. The function ق(س) ق(س) ق(س) is a piecewise function with three different expressions based on the value of س س س.2. We need to graph each piece of the function separately according to its domain.

STEP 2

1. Identify the expressions and their respective domains.2. Graph each piece of the function over its domain.3. Combine the graphs to represent the entire piecewise function.

STEP 3

STEP 4

Graph the first piece ق(س)=س2+2س−6 ق(س) = س^2 + 2س - 6 ق(س)=س2+2س−6 for س≥6 س \geq 6 س≥6: - This is a quadratic function opening upwards. - Plot the graph starting from س=6 س = 6 س=6 and extending to the right.

STEP 5

Graph the second piece ق(س)=−(س2+3س−6) ق(س) = -(س^2 + 3س - 6) ق(س)=−(س2+3س−6) for 1<س<6 1 < س < 6 1<س<6: - This is a quadratic function opening downwards. - Plot the graph between س=1 س = 1 س=1 and س=6 س = 6 س=6.

STEP 6

Graph the third piece ق(س)=س−2 ق(س) = س - 2 ق(س)=س−2 for س≤1 س \leq 1 س≤1: - This is a linear function with a slope of 1. - Plot the graph starting from س=1 س = 1 س=1 and extending to the left.

STEP 7

Combine the graphs from each step to form the complete piecewise function. - Ensure continuity or discontinuity at the boundaries س=1 س = 1 س=1 and س=6 س = 6 س=6 as per the domain restrictions. The graph of the piecewise function ق(س) ق(س) ق(س) is now complete.

Get Studdy

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.

1. The function $ق(س)$ is a piecewise function with three different expressions based on the value of $س$ .
2. We need to graph each piece of the function separately according to its domain.

1. Identify the expressions and their respective domains.
2. Graph each piece of the function over its domain.
3. Combine the graphs to represent the entire piecewise function.

Graph the first piece $ق(س) = س^2 + 2س - 6$ for $س \geq 6$ : - This is a quadratic function opening upwards. - Plot the graph starting from $س = 6$ and extending to the right.

Graph the second piece $ق(س) = -(س^2 + 3س - 6)$ for $1 < س < 6$ : - This is a quadratic function opening downwards. - Plot the graph between $س = 1$ and $س = 6$ .

Graph the third piece $ق(س) = س - 2$ for $س \leq 1$ : - This is a linear function with a slope of 1. - Plot the graph starting from $س = 1$ and extending to the left.

Combine the graphs from each step to form the complete piecewise function. - Ensure continuity or discontinuity at the boundaries $س = 1$ and $س = 6$ as per the domain restrictions.
The graph of the piecewise function $ق(س)$ is now complete.