WRITE THE STEP FUNCTION FROM THE GRAPH
A step function or staircase function is a piecewise function containing all constant "pieces".
The constant pieces are observed across the adjacent intervals of the function, as they change value from one interval to the next.
Two circles can be used to restrict the domain of step function.
○ Open circle, the value cannot be included.
○ is similar to <, >, (, )
● Closed circle, the value can be included.
● is similar to ≤ , ≥, [, ]
Write the step function from the graph given below.
Problem 1 :
Solution :
Domain of the function is [-4, 1).
There are three pieces. From bottom to top.
|
Step functions f(x) = -5 f(x) = -3 f(x) = -1 |
Domain -5 ≤ x < -3 -3 ≤ x < -1 -1 ≤ x < 1 |
So, the required step function is
Problem 2 :
Solution :
Domain of the function is (0, 4].
|
Step functions f(x) = 4 f(x) = 3 f(x) = 2 f(x) = 1 |
Domain 0 < x ≤ 1 1 < x ≤ 2 2 < x ≤ 3 3 < x ≤ 4 |
So, the required step function is
Problem 3 :
Solution :
Domain of the function is [-3, 6)
|
Step functions f(x) = 7 f(x) = 5 f(x) = 1 |
Domain 1 ≤ x < 6 0 ≤ x < 1 -3 ≤ x < 0 |
So, the required step function is
Problem 4 :
Solution :
Domain of the function is [-4, 2)
|
Step functions f(x) = 1 f(x) = 3 |
Domain -4 ≤ x < -1 -1 ≤ x < 2 |
So, the required step function is
Problem 5 :
Solution :
Domain of the function is (-4, 0]
|
Step functions f(x) = 5 f(x) = 4 f(x) = 3 f(x) = 2 |
Domain -4 < x ≤ -3 -3 < x ≤ -2 -2 < x ≤ -1 -1 < x ≤ 0 |
So, the required step function is
Problem 6 :
Solution :
Domain of the function is [-2, 5)
|
Step functions f(x) = -1 f(x) = 1 f(x) = 3 f(x) = 5 |
Domain -2 ≤ x < -1 0 ≤ x < 1 2 ≤ x < 3 4 ≤ x < 5 |
So, the required step function is
Problem 7 :
Solution :
Domain of the function is (-8, 6.5]
|
Step functions f(x) = 4 f(x) = 0.5 f(x) = -2 |
Domain -8 < x < -2 0 < x ≤ 6.5 -2 ≤ x ≤ 0 |
So, the required step function is
Problem 8 :
Evaluate
i) f(-3)
ii) f(-2)
iii) f(1)
Solution :
i) f(-3) = -1
ii) f(-2) = 3
iii) f(1) = 5
Problem 9 :
Solution :
Domain of the function is (-10, 4)
|
Step functions f(x) = 9 f(x) = 5 f(x) = 3 f(x) = -5 |
Domain -10 < x ≤ -5 -5 < x < -3 2 < x ≤ 4 -3 ≤ x ≤ 2 |
So, the required step function is
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