Mathematics
Grade10
Easy

Question

Write a piecewise-defined function for the graph below

  1. f(x) : {(3.5x – 8 , x ≥ 2) , (2x – 3 , x < 2)}
  2. f(x) : {(6x + 7, x ≥ 2) , (-0.6x + 0.8 , x < 2)}
  3. f(x) : {(3.5x – 9, x ≥ 2) , (0.5x – 0.8 , x < 2)}
  4. f(x) : {(2.5x – 7, x ≥ 2) , (-0.6x – 0.8 , x < 2)}

Hint:

In this question, we have to find the piecewise defined function for the given graph i.e., a function in which more than one formula is used to define the output over different pieces of the domain. Firstly, we will consider x ≥ 2 and using the points (4, 3) and (2, -2) to the find the equation of the line. Later, we will consider x< 2 and (-3, 1) and (2, -2) to find the other equation. The function two-equation obtained is the required answer.

The correct answer is: f(x) : {(2.5x – 7, x ≥ 2) , (-0.6x – 0.8 , x < 2)}


    For x ≥ 2, let’s find the equation of the graph:
    General equation of a line: y = mx + c
    Consider the points (4, 3) and (2, -2).
    m = fraction numerator left parenthesis negative 2 comma space minus 3 right parenthesis over denominator left parenthesis 2 comma space minus 4 right parenthesis end fraction = fraction numerator negative 5 over denominator negative 2 end fraction = 5 over 2 = 2.5
    3 = 2.5 × 4 + c (Putting (4, 3) values in a general equation)
    c = 3 – 10 = -7
    Equation: y = 2.5x – 7 for x ≥ 2
    For x < 2, let’s find the equation of the graph:
    General equation of a line: y = mx + c
    Consider the points (-3, 1) and (2, -2).
    m = (-2 – 1)/ (2 – (-3)) = -3 over 5 = -0.6
    -2 = -0.6 × 2 + c (Putting (2, -2) values in general equation)
    c = -2 + 1.2 = -0.8
    Equation: y = -0.6x – 0.8 for x < 2
    f(x): {(2.5x – 7, x ≥ 2), (-0.6x – 0.8, x < 2)}

    Related Questions to study

    card img

    With Turito Academy.

    card img

    With Turito Foundation.

    card img

    Get an Expert Advice From Turito.

    Turito Academy

    card img

    With Turito Academy.

    Test Prep

    card img

    With Turito Foundation.