Math Problem Statement
Знайдіть область значень функції y = x + 3, заданої на проміжку: a) [-3; 3]; b) [1; 7]; в) [0; +∞).
Solution
The problem in the image asks to find the range ("область значень") of the function , given different domains of .
Let's go through each part:
Function:
Part (a): Domain
If is between and , we substitute these values into the function:
- When ,
- When ,
Thus, the range is .
Part (b): Domain
For between and , we calculate:
- When ,
- When ,
So, the range is .
Part (c): Domain
For , the function becomes:
- When ,
- As increases, increases without bound.
Thus, the range is .
Would you like more details on any part of the solution?
Here are 5 related questions to consider:
- What would the range be if the domain was ?
- How does shifting the function affect the range compared to ?
- What happens to the range if we change the function to ?
- Can the range of this linear function ever be restricted to a finite interval?
- How does the slope of the function influence the range?
Tip: For linear functions like , the slope and the intercept define how the function behaves over any domain, making range calculations straightforward.
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Math Problem Analysis
Mathematical Concepts
Linear Functions
Domain and Range
Formulas
y = x + 3
Theorems
Basic properties of linear functions
Suitable Grade Level
Grades 8-10