Respuesta :

So we know

[tex]\\ \rm\rightarrowtail y=ab^x[/tex]

Put what's given

[tex]\\ \rm\rightarrowtail -3=ab^0[/tex]

[tex]\\ \rm\rightarrowtail -3=a[/tex]

Now put back

[tex]\\ \rm\rightarrowtail y=-3b^x[/tex]

  • Range of all y values less than 0

  • turn b to Euler's number then
  • As we know that e^x has range (0,oo) when multiplied with any negative number i.e here -3 it yields y less than 0

[tex]\\ \rm\rightarrowtail y=-3e^x[/tex]

Graph attached

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semsee45

Answer:

General form of an exponential function:  [tex]y=ab^x[/tex]

where:

  • [tex]a[/tex] is the y-intercept (or initial value)
  • [tex]b[/tex]  is the base (or growth factor)
  • [tex]x[/tex]  is the independent variable

If [tex]b > 1[/tex]  then it is an increasing function

If [tex]0 < b < 1[/tex] then it is a decreasing function

Also [tex]b\neq 1[/tex]

Given:

  • y-intercept = (0, -3)

[tex]\implies y=(-3)b^x[/tex]

If we want the function to be decreasing, then as [tex]a[/tex] is negative, we need [tex]b > 1[/tex] to make the overall function decreasing.  

Let [tex]b=2[/tex] :

[tex]\implies y=(-3)2^x[/tex]

If we want the function to be increasing, then as [tex]a[/tex] is negative, we need [tex]0 < b < 1[/tex] to make the overall function increasing.

Let [tex]b=\dfrac12[/tex] :

[tex]\implies y=-3\left(\dfrac12\right)^x[/tex]

However, it doesn't matter whether the function is increasing or decreasing as the range of both of the above given functions is < 0 as [tex]a[/tex] is negative and [tex]b[/tex] is positive.

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