How do you graph $f (x) = 2^{x - 1} - 3$ $f(x)=2^(x-1)-3$ and state the domain and range?

Question

3194 views around the world

You can reuse this answer
Creative Commons License

Answer 1 · 2018-02-03T14:27:36

**Domain: ** $(- \infty, \infty)$ $(-oo, oo)$

**Range: ** $f (x) > (- 3)$ $f(x)>(-3)$

Given:

$y = f (x) = 2^{x - 1} - 3$ $color(blue)(y = f(x) =2^(x-1)-3)$

Refer to the graph below to understand the behavior of the given exponential function:

graph{2^(x-1)-3 [-10, 10, -5, 5]}

Let us look at the table given below:

enter image source here

We observe that the domain will be all real values.

For every value of $x$ $x$ there is a corresponding $y$ $y$ value.

Hence

Domain: $(- \infty, \infty)$ $(-oo, oo)$

Below you find a representation of both the parent function $y = 2^{x} and y = 2^{x - 1} - 3$ $color(green)(y=2^x and y = 2^(x-1)-3$

enter image source here

We find a horizontal asymptote at $y = - 3$ $y=-3$

Hence **Range: ** $f (x) > (- 3)$ $f(x)>(-3)$

How do you graph f(x)=2^(x-1)-3f(x)=2x−1−3f(x)=2^(x-1)-3 and state the domain and range?