Question

Name 3 of the 4 features listed below for the function g(x)=log2(x*4)-1 and include a description of how you found those answers using complete sentences.
1. Vertical Asymptote
2. Domain
3. X and Y Intercepts
4. Transformations compared to its parent function f(x)=log2x

Answer 1

Answer:

1. x=0

2. x>0

3. X-intercept: (0.5,0) Y-intercept: undefined

4. Compressed horizontally by a factor of 0.25 and shifted 1 unit down.

Step-by-step explanation:

1. The given parent function is $f(x)=\log_2x$

The transformed function is $g(x)=\log_2(x*4)-1$

The vertical asymptote is x=0.

We find this by equating the argument to zero. 4x=0----->x=0

2. The domain is all values of x that make the function defined.

The domain is $x\:>\:0$

3. To find x-intercept we substitute g(x)=y=0 and solve for x.

$\log_2(x*4)-1=0$

$\log_2(x*4)=1$

$(x*4)=2^1$

$4x=2$

x=0.5

The x-intercept is (0.5,0)

The y-intercept is undefined because we have to substitute x=0, which is not in the domain of g(x).

4. We can rewrite the transformed function in terms of f(x) as

$g(x)=f(4x)-1$

This means there is a horizontal compression by $\frac{1}{4}$ and shift 1 unit down of the parent function.