Question

In Problems 29–40:

$f\left(x\right)=2int\left(x\right)$

1. Find the domain of each function.
2. Locate any intercepts.
3. Graph each function.
4. Based on the graph, Find the range.
5. Isf continuous on its domain?

Short answer

1. The domain of the function is all real numbers. .
2. The x-intercepts is $(x,0)$for $0\le x<1$.
3. The graph of the function is as follows,
4. The range of the function is the set of even integers.
5. The functionf is not continuous

Step-by-step solution

Step 1. Given Information   

We are given a function,

$f\left(x\right)=2int\left(x\right)$

Part(a) Step 1. Finding the domain of the function   

The domain of function$f\left(x\right)=2int\left(x\right)$ is all real numbers.

Part(b) Step 1. Locating intercepts  

The x-intercepts are those points for which the y -coordinate is zero and the y-intercepts are those points for which the x-coordinate is zero.

The value of function is zero when $0\le x<1$

So. thex-intercept is$(x,0)$for$0\le x<1$

Part(c) Step 1. Graphing the function  

The table of values for graphing the function is as follows,

The graph is as follows,

Part(d) Step 1. Finding the range  

As seen from the graph, the range of the function is the set of even integers.

Part(e) Step 1. Checking continuity  

The function f is not continuous because it is discontinuous at$\left\{x\right|xisaninteger\}$