Math Problem Statement
Solution
To determine the domain on which this function is decreasing, we observe the graph. The function appears to be a parabola opening upwards, indicating a quadratic function. For a parabola of this nature, the function is decreasing on the left side of the vertex (the lowest point) and increasing on the right side of the vertex.
In this graph:
- The vertex of the parabola is at .
- The function decreases as moves from to .
Thus, the domain on which the function is decreasing is:
Would you like more details or have any questions?
Here are some related questions:
- How do you determine the vertex of a parabola from its equation?
- What characteristics of a quadratic function indicate where it increases or decreases?
- Can a function have multiple intervals of increase and decrease?
- How can the first derivative test confirm intervals of increase or decrease?
- What is the significance of the axis of symmetry in determining where a function is increasing or decreasing?
Tip: For quadratic functions, identifying the vertex is key to determining intervals of increase and decrease.
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Math Problem Analysis
Mathematical Concepts
Algebra
Quadratic Functions
Graph Analysis
Formulas
Standard form of a quadratic function f(x) = ax^2 + bx + c
Theorems
Vertex theorem for quadratic functions
Suitable Grade Level
Grades 9-10
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