Mathematics
Grade10
Easy

Question

What is the equation of this graph?

  1. f(x) = fraction numerator 1 over denominator left parenthesis straight x space plus space 3 right parenthesis end fraction + 5
  2. f(x) = fraction numerator 1 over denominator left parenthesis straight x space minus space 5 right parenthesis end fraction+ 3
  3. f(x) = fraction numerator 1 over denominator left parenthesis straight x space plus space 5 right parenthesis end fraction - 3
  4. f(x) = fraction numerator 1 over denominator left parenthesis straight x space minus space 3 right parenthesis end fraction – 5 

Hint:

Graph transformation is the process by which an existing graph, or graphed equation, is modified to produce a variation of the proceeding graph.

The correct answer is: f(x) = fraction numerator 1 over denominator left parenthesis straight x space minus space 5 right parenthesis end fraction+ 3


    Here, we have to find the equation of the given graph.
    Here, f(x) = straight k over straight x has shifted 3 units up and 5 units to the right.
    3 units up means: output (f(x)) increased by 3 units
    5 units to the right: input (x) decreased by 5 units
    So, f(x) = fraction numerator k over denominator left parenthesis straight x space minus space 5 right parenthesis end fraction + 3
    As we can see, the graph passes through (4, 2).
    2 = fraction numerator straight k over denominator left parenthesis negative 1 right parenthesis end fraction + 3
    k = 1
    Equation: f(x) = fraction numerator 1 over denominator left parenthesis straight x space minus space 5 right parenthesis end fraction + 3.
    Hence, the correct option is D.

    There are many ways to transform a graph such as vertical translation, vertical stretch, horizontal translation and horizontal stretch.

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