Question

In two or more complete sentences, describe the transformation(s) that take place on the parent function, f(x) = log(x), to achieve the graph of g(x) = log(-2x-4) + 5

Please solve this for me!!!!

Answer 1

Explanation:

Howdy there :)

To describe the transformation of the parent logarithmic function, you just need to follow these rules

1. A + on the outside of the parentheses will mean a vertical shift upwards. As such, the transformation is moved 5 units up. If it was -, it would move 5 units down.

2. The inside of the parentheses will result in a horizontal shift right 4 units. The rule to remember is that these kinds of functions follow x(a - b) rules, meaning that when the 4 is subtracted, we are really talking about a positive four, unlike in standard arithmetic. Vice versa, a + 4 will mean a -4 four, since a - -4 is the same as a + 4. As such, we will move in the positive direction (right) on the y axis.

3. Since x is now -2x, we are reflecting about the y axis, meaning the function will switch from left to right or right to left.

4. The 2 in front of it represents a vertical dilation by a factor of 2. This is because our constant, 2, is greater than 1. If the number were in between 0 and 1, it would represent a vertical compression by the constant number.