Question

Graph each function. Find the y-intercept, and state the domain and range.

$\mathit{y}\mathbf{=}{\mathbf{2}}^{\mathbf{x}}\mathbf{-}\mathbf{3}$

Short answer

The graph of the function is:

y-intercept is $\mathbf{(}\mathbf{0}\mathbf{,}\mathbf{-}\mathbf{2}\mathbf{)}$and domain is all real number and range is $\mathit{y}\mathbf{>}\mathbf{-}\mathbf{3}$.

Step-by-step solution

Step 1. Graph the equation.

Graph of the function: $y=2^x-3$

Step 2. Find the y-intercept.

The $y$-intercept of a graph is the point where the graph intersects the $y$-axis that is., $x$-coordinate of a $y$-intercept is 0. So, to find $y$-intercept substitute 0 for $x$into the equation.

$y=2^x-3$

$\begin{array}{l}y=2^x-3\\ =2^0-3[x=0]\\ =1-3\\ =-2\end{array}$

Thus, y–intercept is $y=-2$.

Step 3. Find the range and domain.

The domain of a function$f\left(x\right)$is the set of all values for which the function is defined, and the range of the function is the set of all values that $f$takes.

From the graph, it can be concluded that domain is all real number and range is $y>-3$.