Question

What is the y-intercept of the exponential function? f(x)=−32(2)x−3+3 Enter your answer in the box.

Answer 1

y-intercept for x = 0.

Substitute x = 0 to the equation of the function:

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

Answer 2

Answer:

-1

Step-by-step explanation:

We are given that a function

$f(x)=-32(2)^{x-3}+3$

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

$f(0)=-32(2)^{0-3}+3$

$f(0)=-32(2)^{-3}+3$

$f(0)=-\frac{32}{(2)^3}+3$

By using property $a^{-x}=\frac{1}{a^x}$

$f(0)=-\frac{32}{8}+3$

$f(0)=-4+3=1$

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