Q45. - Algebra 1

Question

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

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

Step-by-Step Solution

Answer

The graph of the function is:

$\mathit{y}$-intercept is $\mathbf{(}\mathbf{0}\mathbf{,}\mathbf{1}\mathbf{)}$ and domain is all real number and range is$\mathit{y}\mathbf{>}\mathbf{0}$.

Step 1. Graph the equation.

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

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$y=2^x$.

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

Thus, $y$–intercept is $y=1$.

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 $y>0$.