Question

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

$y=2{\left(5\right)}^x$

Short answer

The graph of the function is:

y-intercept is$\left(0,2\right)$and domain is all real number and range is$y>0$.

Step-by-step solution

Step 1. Graph the equation.

Graph of the function:$y=2{\left(5\right)}^x$

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 $y=2{\left(5\right)}^x$.

$$\begin{gathered} y=2{\left(5\right)}^x \\ =2{\left(5\right)}^0\left[x=0\right] \\ =2 \end{gathered}$$

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 $y>0$.