#### To determine

**To find:** To find the domain and range of the function f(x)=lnx+2.

#### Answer

The domain of the function is (0 ,∞) and the range of the function is (-∞,∞).

#### Explanation

**Calculation:**

**Step 1:** First we will find the domain of y=lnx+2.

**Step 2:** We know that the domain of lnx is (0,∞) and 2 is a constant function with domain

(-∞,∞).

**Step 3:** So, the domain of the function f(x)=lnx+2 is the intersection of (0,∞) and (-∞,∞) i.e.

(0,∞).

**Step 4:** Now, we will find the range of the function f(x)=lnx+2.

We know that the range include all values of *f(x)* for which there is some *x* such that fx=

lnx+2. The range of the function fx=lnx+2 is all the real number (-∞,∞).

**Final statement:**

The domain of the function is (0 ,∞) and the range of the function is (-∞,∞).

#### To determine

**To find:** *x-* intercept of the graph of f.

#### Answer

*x-* intercept of the graph of f is ≈0.135.

#### Explanation

**Calculation:**

To find the *x-*intercept of the graph of *f*, we have to find the value of x for which

fx=0 that is

lnx+2=0

or lnx=-2.

Now, we take the exponential function of both sides which is the inverse function of the

logarithmic function. Thus

elnx=e-2

Since we know that

elnx=x (1)

From equation (1) we have

x=e-2. Now using scientific calculator, we can calculate the value of x up to 3 decimal places.

So, the approximate value of x-intercept up to 3 decimal places is x≈0.135.

**Final statement:**

*x-* intercept of the graph of f is ≈0.135.

#### To determine

**To find:** Sketch the graph of f.

#### Answer

See the graph

#### Explanation

*Explanation:*

To sketch the graph of f(x)=lnx+2, first we draw the graph of f(x)=lnx( as given in Figure 3)

and then using the transformation gx=fx+2. Thus, we will get the graph of fx=

lnx+2, by shifting the graph of x=lnx, 2 points upward. So, the graph of fx=

lnx+2 is

**Final statement:**

See the graph