Question

In the problems below, f(x) = log2x and g(x) = log10x. How are the graphs of f and g similar? Check all that apply. Both have a y-intercept of 1. Both increase from left to right. Both have an asymptote of x = 0. Both have a domain of all real numbers.

Answer 1

Answer:

1st part: 2nd and 3rd answers

2nd part: 1,0

3rd part: f

Answer 2

Answer:

Both increase from left to right

Both have an asymptote of x=0

Step-by-step explanation:

The The graph of $\log(2x)$ si shown in red in the image attached. The graph of  $\log(10x)$  is shown in blue in the attached image.

Statement 1: From these graphs we can see non of these graphs cross the y axis at 1, as a mater of fact, the log function can not touch the y axis so the first statement is incorrect.

Statement 2: From the graphs, we can tell that both graphs increase from left to right. This is indeed true for logarithmic functions. They increase with increasing values of x.

Statement 3: This statement is true. This statement is true because  non of these graphs come can cross the y axis, i.e the logarithm of a zero is not defined. What  log functions do is approach the y axis but never touch it.

Statement 4: This statement is incorrect. The domain of both functions is all values of x that are greater than zero. This is true for all logarithmic functions.