By applying the concept of Translation in functions, it is determined that the graph of [tex]\frac{1}{3} f(x)[/tex] is narrower than the graph of [tex]f(x)[/tex] and the graph of [tex]f(x)-4[/tex] is 4 units down from the graph of [tex]f(x)[/tex].
It is given to us that there is a graph of -
[tex]f(x) = x^{2} -2[/tex] -----(1)
We have to find out the comparison between the graphs of [tex]\frac{1}{3} f(x)[/tex] and [tex]f(x)-4[/tex] with the graph of [tex]f(x)[/tex] ----- (2)
We have to make use of Translation concepts in order to do the necessary comparison.
- A Translation is defined by any changes in the given function graph
- These changes can be observed in the form of addition or subtraction or multiplication in the definition of the function.
According to the given question,
- The graph of [tex]\frac{1}{3} f(x)[/tex] is obtained by multiplying 1/3 with the graph of[tex]f(x)[/tex]. Thus, the graph of [tex]\frac{1}{3} f(x)[/tex] is narrower than the graph of [tex]f(x)[/tex].
- The graph of [tex]f(x)-4[/tex] is obtained by shifting the graph of [tex]f(x)[/tex] up to 4 units down. Thus, the graph of [tex]f(x)-4[/tex] is 4 units down from the graph of [tex]f(x)[/tex].
Thus, through Translation in functions we have found out that the graph of [tex]\frac{1}{3} f(x)[/tex] is narrower than the graph of [tex]f(x)[/tex] and the graph of [tex]f(x)-4[/tex] is 4 units down from the graph of [tex]f(x)[/tex].
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