Question

Sketch the graph of the function $y=-2.5{\left(5\right)}^x$. Then state the function’s domain and range.

Short answer

The domain of the function $y=-2.5{\left(5\right)}^x$ is $\left(-\infty ,\infty \right)$ and range is $\left(-\infty ,0\right)$ whose graph is shown below.

Step-by-step solution

Step 1. Write down the given information.

The given function is $y=-2.5{\left(5\right)}^x$.

Step 2. Sketch the graph for the given function.

The graph for the function $y=-2.5{\left(5\right)}^x$ using the graphing calculator is shown below.

Step 3. Interpretation from the graph.

From the graph it can be seen that,

x can take all the values from $-\infty \text{to}\infty$and ytakes all the negative values from $-\infty \text{to}0$ excluding 0.

Therefore, the domain of the function $y=-2.5{\left(5\right)}^x$ is $\left(-\infty ,\infty \right)$ and range of the function is $\left(-\infty ,0\right)$.