Q 63. - Precalculus Enhanced with Graphing Utilities

Question

(a) graph each function, (b) determine the domain and the range of the function, and (c) determine where the function is increasing and where it is decreasing.

$F\left(x\right)=2x-5$

Step-by-Step Solution

Answer

Part (a). The required graph is:

Part (b). The domain and range of the given function is all real numbers or $\left(-\infty ,+\infty \right)$.

Part (c). The function is increasing in the whole domain.

Part (a) Step 1. Given information.

The given function is $F\left(x\right)=2x-5$.

Part (a) step 2. Draw the graph.

Part (b) Step 1. Given information.

The given linear function is $F\left(x\right)=2x-5$.

Part (b) Step 2. Determine the domain and range of the given function.

From the above graph, the domain and range of the function is all real numbers.

Part (c) Step 1. Given information.

The given function is $F\left(x\right)=2x-5$.

Part (c) Step 2. Determine where the function is decreasing and increasing.

From the above graph, as we increase the value of the $x$, the value of the function increases. So, the function is increasing all the time.

Hence, the function is increasing in the whole domain.