Respuesta :

gmany

y-intercept for x = 0.

Substitute x = 0 to the equation of the function:

[tex]f(x)=-32(2)^{x-3}+3\\\\f(0)=-32(2)^{0-3}+3=-32(2)^{-3}+3=-32\cdot\dfrac{1}{2^3}+3=-32\cdot\dfrac{1}{8}+3\\\\=-4+3=-1\\\\Answer:\ \boxed{y-intercept=-1\to(0,\ -1)}[/tex]

lublana

Answer:

-1

Step-by-step explanation:

We are given that a function

[tex]f(x)=-32(2)^{x-3}+3[/tex]

We have to find the y- intercept of the exponential function.

To find the y- intercept of given exponential we will substitute x=0

Substitute x=0 then, we get

[tex]f(0)=-32(2)^{0-3}+3[/tex]

[tex]f(0)=-32(2)^{-3}+3[/tex]

[tex]f(0)=-\frac{32}{(2)^3}+3[/tex]

By using property [tex]a^{-x}=\frac{1}{a^x}[/tex]

[tex]f(0)=-\frac{32}{8}+3[/tex]

[tex]f(0)=-4+3=1[/tex]

Hence, the y- intercept of given exponential =-1

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