Mathematics
Grade10
Easy
Question
Write a piecewise-defined function for the graph below
- f(x) : {(3x – 5 , x ≥ 1) , (0.5x + 4 , x < 1)}
- f(x) : {(3x – 5 , x < 1) , (0.5x + 4 , x ≥ 1)}
- f(x) : {(-2x + 6 , x <1) , (0.5x + 3.5 , x ≥ 1)}
- f(x) : {(-2x + 6, x ≥ 1) , (0.5x + 3.5 , x < 1)}
Hint:
The equation of a straight line is a mathematical equation that gives the relation between the coordinate points lying on that straight line. It can be written in different forms and tells the slope, x-intercept, and y-intercept of the line.
The correct answer is: f(x) : {(-2x + 6, x ≥ 1) , (0.5x + 3.5 , x < 1)}
For x ≥ 1, let’s find the equation of the graph:
General equation of a line: y = mx + c
Consider the points (1, 4) and (4, -2).
m = 
= 
= -2
4 = -2 × 1 + c (Putting (1,4) values in general equation)
c = 4 + 2 = 6
Equation: y = -2x + 6 for x ≥ 1
For x < 1, let’s find the equation of the graph:
General equation of a line: y = mx + c
Consider the points (-3, 2) and (1, 4).
m =
= 
= 0.5
2 = 0.5× (-3) + c (Putting (-3,2) values in general equation)
c = 2 + 1.5 = 3.5
Equation: y = 0.5x + 3.5 for x < 1
f(x) : {(-2x + 6 , x ≥ 1), (0.5x + 3.5 , x < 1)}
The most commonly used forms of the equation of straight line are y = mx + c and ax + by = c. Some other forms are point-slope form, slope-intercept form, general form, standard form, etc.
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