Math Problem Statement
(a) For the linear function ( f(x)=x+5 ), evaluate ( f(-2) ) and ( f(4) ).
(b) Graph ( f ). How can the graph of ( f ) be used to determine the zero of ( f ) ?
(c) Find the zero of ( f ).
(a) ( f(-2)= ) ( \square )
(Type an integer or a fraction.)
Solution
Let's work through the problem step by step.
Part (a): Evaluate and .
The linear function is given by .
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Evaluate :
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Evaluate :
So:
Part (b): Graph
The graph of is a straight line with a slope of 1 and a y-intercept at .
Using the Graph to Determine the Zero of :
The zero of the function is the value of where . On the graph, this is the point where the line crosses the x-axis.
Part (c): Find the Zero of
To find the zero, set and solve for :
So, the zero of the function is .
Summary:
- (a)
- (b) The graph of crosses the x-axis at .
- (c) The zero of is .
Would you like further details on any part of this solution?
Here are five related questions you might explore:
- What is the slope of the function ?
- How does changing the value of the constant term (e.g., instead of ) affect the graph?
- What is the y-intercept of the function ?
- How would you find the zero of the function ?
- What does the zero of a function represent in a real-world context?
Tip: The slope of a linear function tells you how steep the line is, while the y-intercept indicates where the line crosses the y-axis.
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Math Problem Analysis
Mathematical Concepts
Linear Functions
Graphing
Zero of a Function
Formulas
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Theorems
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Suitable Grade Level
Grades 7-9