Math Problem Statement
graph f(x)=-3|1/2x-1| -11 give me ponits
Solution
To graph the function , we proceed by analyzing and selecting appropriate points.
Step-by-Step Breakdown:
-
Vertex Calculation:
The expression inside the absolute value becomes zero at . Solving for ,
So, the vertex of the graph is at . -
Behavior Left and Right of the Vertex:
-
For ,
Therefore,
Simplifying,
-
For ,
Therefore,
Simplifying,
-
Selected Points:
-
Vertex:
-
To the left of the vertex:
- At ,
So, - At ,
So,
- At ,
-
To the right of the vertex:
- At ,
So, - At ,
So,
- At ,
Table of Points:
0 | -14 |
1 | -12.5 |
2 | -11 |
3 | -12.5 |
4 | -14 |
Would you like a plot of this graph or further analysis?
Follow-up Questions:
- What are the steps for finding the vertex of any absolute value function?
- How does the slope change before and after the vertex?
- Why does the graph form a "V" shape instead of a straight line?
- How would shifting the function vertically affect the graph?
- Can you explain the role of the negative sign in front of the absolute value here?
Tip:
Remember, the vertex of an absolute value graph is always located where the inside of the absolute value equals zero.
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Math Problem Analysis
Mathematical Concepts
Algebra
Absolute Value Functions
Graphing Piecewise Functions
Formulas
Vertex of absolute value function: x = h when |ax - h| = 0
Piecewise function for absolute value: f(x) = a|bx - c| + d
Slope-intercept form: y = mx + b
Theorems
Definition of Absolute Value
Transformation of Absolute Value Functions
Suitable Grade Level
Grades 9-11
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