SOLUTION: Describe the transformations on the following graph of f(x)=log(x). State the placement of the vertical asymptote and x-intercept after the transformation. For example, �le

Question 116019: Describe the transformations on the following graph of f(x)=log(x).

State the placement of the vertical asymptote and x-intercept after the transformation. For example, �left 1� or �stretched vertically by a factor of 2� are descriptions.

a) g(x)=log(x+2)
Answer by jim_thompson5910(35256) (Show Source): You can put this solution on YOUR website!
a)

From the graph of , we can see that only positive x values will work. In other words, the domain of f is (0,

). Now let's find the domain of :

Set the inner expression greater than zero

Subtract 2 from both sides

Combine like terms on the right side

So that means x must be greater than -2
So here is the domain in interval notation: (-2,

)

Notice how the endpoint of the domain has been shifted to the left two units. So what this did was simply shift every x value 2 units to the left

----------------------------------
Answer:
So the transformation shifts the entire graph of two units to the left

Notice if we graph and , we get

Graph of (red) and (green)

and we can visually verify the transformation

Vertical Asymptote:

From the graph, we can see that the vertical asymptote is for . Since we've shifted the graph 2 units to the left, we've also shifted the vertical asymptote 2 units to the left.

----------------------------------
Answer:
So the vertical asymptote for is

We can visually verify this if we look at the graph above

x-intercept in (x, y) form:

From the graph, we can see that the x-intercept of is (1,0). Since we've shifted everything two units to the left, the x-intercept shifts two units to the left also.

So subtract 2 from 1 to get

(1-2,0)---->(-1,0)

----------------------------------
Answer:
So the x-intercept of is (-1,0)

Once again, we can visually verify this if we look at the graph above
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