EXPONENTIAL FUNCTIONS HELP Write the function for each graph described below. the graph of f(x) = 2x reflected across the x-axis. The graph of f(x)= 1/3x translated up 5 units. The graph of f(x) = 3x left 2 units, and down 3. The graph of f(x) = 1/2x translated down 2 units. The graph of f(x) = 4x stretched horizontally by a factor of 3. The graph of f(x) = 2x up 4 units, right 3.

Step-by-step explanation:

In general, the transformation ...

  g(x) = f(x -h) +k

translates f(x) right h units and up k units.

The transformation ...

  g(x) = f(x/a)

stretches the graph horizontally by a factor of "a".

The transformation ...

  g(x) = -f(x)

causes the graph to be reflected over the x-axis.

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Applying the above, we have ...

f(x) = 2^x reflected over x is g(x) = -2^x

f(x) = (1/3)^x translated up 5 is g(x) = (1/3)^x +5

f(x) = 3^x translated by (-2, -3) is g(x) = 3^(x +2) -3

f(x) = (1/2)^x translated down 2 is g(x) = (1/2)^x -2

f(x) = 4^x stretched horizontally by a factor of 3 is g(x) = 4^(x/3)

f(x) = 2^x translated by (3, 4) is g(x) = 2^(x -3) +4

solution:

the given function is ,

      =

the three roots of this quadratic function is , 0 ,8 and 10.all the roots are real and rational.

if a quadratic equation is of the form ,

sum of the roots = a + b +c= 0+8+10=18=  

product of roots taken two at a time = a b + b c+ c a = 0+80+0=80 =  

product of roots = a b c = 0=  

there are 11 doors in a hall starting from 0 to 11.the entry in the hall is permitted through gate number 0 and exit is allowed through only gate number 8 and 10.so, three roots(0,8,10) of quadratic function is given by entry and exit route of this hall.