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Zhang is planning a ski trip. The equation C = 200 + 23g models the relation between the cost in dollars, C, of the ski trip and the number of skiers, g. Find thr cost is the number of skiers is 20. The cost is ____   2) Identify the relations that represent functions from the image titled "functions".   3) Evaluate i(-3) if i(x) = 2x^2 - 4x + 6

Zhang is planning a ski trip. The equation C = 200 + 23g models the relation between the cost in dollars, C, of the ski trip and the number of skiers, g. Find thr cost is the number of skiers is 20. The cost is ____   2) Identify the relations that represent functions from the image titled "functions".   3) Evaluate i(-3) if i(x) = 2x^2 - 4x + 6

Algebra & Trigonometry with Analytic Geometry
Algebra & Trigonometry with Analytic Geometry
13th Edition
ISBN:9781133382119
Author:Swokowski
Publisher:Swokowski
Chapter11: Topics From Analytic Geometry
Section11.2: Ellipses
Problem 34E
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1) Zhang is planning a ski trip. The equation C = 200 + 23g models the relation between the cost in dollars, C, of the ski trip and the number of skiers, g.

Find thr cost is the number of skiers is 20.

The cost is ____

 

2) Identify the relations that represent functions from the image titled "functions".

 

3) Evaluate i(-3) if i(x) = 2x^2 - 4x + 6

 

 

 

 

## Identifying Functions Among Relations ### Task Select all of the following relations that represent functions. ### Graph Descriptions #### Top Left Graph - **Shape:** Ellipse - **Coordinates:** The ellipse spans from approximately (1, -3) to (3, 3). - **Axes:** The x-axis ranges from -1 to 5, and the y-axis from -4 to 4. - **Observation:** Use the vertical line test to determine if this is a function. #### Top Right Graph - **Shape:** Diagonal Line - **Coordinates:** The line descends from point (-2, 4) to point (2, -2). - **Axes:** The x-axis ranges from -2 to 2.5, and the y-axis from -2 to 4. - **Observation:** Use the vertical line test to determine if this is a function. #### Bottom Left Graph - **Shape:** Sinusoidal Curve - **Coordinates:** The wave-like curve fluctuates between points (-1, -5) and (5, 5). - **Axes:** The x-axis ranges from -5 to 5.5, and the y-axis from -5 to 5.5. - **Observation:** Use the vertical line test to determine if this is a function. #### Bottom Right Graph - **Shape:** Parabola - **Coordinates:** The parabola opens upwards from its vertex at (2, 0) and spans vertically. - **Axes:** The x-axis ranges from -1 to 5, and the y-axis from -1 to 4. - **Observation:** Use the vertical line test to determine if this is a function. ### Vertical Line Test To determine if a relation represents a function, use the vertical line test. If a vertical line crosses the graph more than once, then the relation is not a function. ### Analysis - **Ellipse (Top Left):** A vertical line intersects the ellipse at two points, indicating it is **not** a function. - **Diagonal Line (Top Right):** A vertical line intersects the line at only one point along its length, indicating it **is** a function. - **Sinusoidal Curve (Bottom Left):** A vertical line may intersect the curve at multiple points along its path, indicating it is **not** a function. - **Parabola (Bottom Right):** A vertical line intersects the parabola
Transcribed Image Text:## Identifying Functions Among Relations ### Task Select all of the following relations that represent functions. ### Graph Descriptions #### Top Left Graph - **Shape:** Ellipse - **Coordinates:** The ellipse spans from approximately (1, -3) to (3, 3). - **Axes:** The x-axis ranges from -1 to 5, and the y-axis from -4 to 4. - **Observation:** Use the vertical line test to determine if this is a function. #### Top Right Graph - **Shape:** Diagonal Line - **Coordinates:** The line descends from point (-2, 4) to point (2, -2). - **Axes:** The x-axis ranges from -2 to 2.5, and the y-axis from -2 to 4. - **Observation:** Use the vertical line test to determine if this is a function. #### Bottom Left Graph - **Shape:** Sinusoidal Curve - **Coordinates:** The wave-like curve fluctuates between points (-1, -5) and (5, 5). - **Axes:** The x-axis ranges from -5 to 5.5, and the y-axis from -5 to 5.5. - **Observation:** Use the vertical line test to determine if this is a function. #### Bottom Right Graph - **Shape:** Parabola - **Coordinates:** The parabola opens upwards from its vertex at (2, 0) and spans vertically. - **Axes:** The x-axis ranges from -1 to 5, and the y-axis from -1 to 4. - **Observation:** Use the vertical line test to determine if this is a function. ### Vertical Line Test To determine if a relation represents a function, use the vertical line test. If a vertical line crosses the graph more than once, then the relation is not a function. ### Analysis - **Ellipse (Top Left):** A vertical line intersects the ellipse at two points, indicating it is **not** a function. - **Diagonal Line (Top Right):** A vertical line intersects the line at only one point along its length, indicating it **is** a function. - **Sinusoidal Curve (Bottom Left):** A vertical line may intersect the curve at multiple points along its path, indicating it is **not** a function. - **Parabola (Bottom Right):** A vertical line intersects the parabola
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